It is easy to underestimate Sofia Coppola. There's her last name, shining like a stoplight, encouraging doubt: how could the daughter of Francis Ford Coppola, one of the most important American filmmakers of all time, live up to the standard set by her father? Is Sofia one more bad case (there have been enough) of nepotism taking someone where talent could not? There was her notorious performance in ''Godfather III,'' and, right after that . . . well, she drifted into the gossip pages. And Sofia, unlike her father, is not an outsize, force-of-nature personality. At 32, she seems years younger: she's slight and girlish, and her manner is almost dreamy, as if she were not fully awake.

But the career arc of Sofia Coppola has upended expectations. Her second feature film, ''Lost in Translation,'' which she wrote and directed, and which opens in mid-September, has already generated a great deal of excitement in the independent-film community and also in Hollywood, with talk that Bill Murray's performance should earn him an Academy Award nomination. ''Lost in Translation'' is no ordinary American film or typical independent film. With its subtleties of character; its strange, luminous pictorial beauty (especially in its distillation of Tokyo); its literary attention to telling detail; its unforced blending of comedy and sadness; and its dreamy intimacy, the film summons place and sustains mood as few contemporary films do. It also hints, in everything from the set to the soundtrack, at a finely tuned sensibility, a high-low, here-there globalism. When Murray's character, a disillusioned movie star in Japan to shoot a whiskey commercial, sings the old Roxy Music song ''More Than This'' in a late-night karaoke bar, he fuses cultures and generations, to say nothing of earnestness and camp. It's thrilling, and new.

Coppola's first feature film, ''The Virgin Suicides,'' which she made five years ago, is increasingly seen as a precocious debut and, among many young women, as a generational statement about suburban life, first love and sexual awakening. Francis Ford Coppola may have started out as a director of small films (''The Rain People,'' one of his earliest films, was an intimate character study), but his greatest triumph was ''The Godfather,'' a large-scale studio movie. Where her father's great themes -- the struggles of Man and Patriarchies in the Modern World -- are vast and epic, Sofia's themes, like the happenstance encounters and quiet epiphanies that can haunt the rest of your life, are more intimate, if no less profound. She doesn't sweep across history or build to dramatic climaxes like her father but rather has her camera search out meaning in small details. She writes scripts that establish, sustain and then gently shift tone and atmosphere -- not Tolstoy but Chekhov. Her films are sophisticated and plangently romantic, and the emotions she stirs up linger. It is perhaps not too much to say that she is the most original and promising young female filmmaker in America.

Among those most convinced of her talents are the people who have worked with her. For her movies, Coppola doesn't simply employ a crew. Rather, she calls on a network of creative people. Some are friends of her father -- for instance, the producer Fred Roos, who worked on almost all of her father's films, and who encouraged her to cast Josh Hartnett, then unknown, for the pivotal role of the heartthrob Trip Fontaine in ''The Virgin Suicides.'' Others are her own friends, many of whom she took with her to Tokyo to shoot ''Lost in Translation'': the cinematographer Lance Acord, whom she met years ago on a photo shoot with the photographer Bruce Weber, and Brian Reitzell, whom she met when he was drumming with the L.A. punk-pop band Redd Kross, and who now produces the soundtracks for her films. And to persuade Bill Murray to take the lead role in her movie, she enlisted her friend Wes Anderson, who directed Murray in two of his films. As Anderson sees it, what holds this network of Coppola's together is her taste -- which is an amalgam of their tastes -- and her talent, which encompasses letting them do what they do best. ''Sofia has uniquely great taste,'' Anderson says, which, given the way Coppola works, is at once a compliment to her and himself.

Although her father fosters a familial atmosphere on most of his sets, he, like most directors, has a god complex. Sofia Coppola is much less dictatorial: soft-spoken, a listener, an encourager of those around her. Which is not to say that she does not get exactly what she wants. ''Don't let Sofia's littleness and quietness confuse you,'' Bill Murray told me recently. ''Sofia is made of steel. She's tough, but she doesn't pretend to be a man. She has a way of getting her way. She's very polite about it. She nods her head and says, 'You're right, you're right, but this is what I want to do.' And it works. When you see her movies, you forget that she is Francis's daughter. She has been able to reinvent what her last name represents.''

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Sofia Coppola would not argue with Murray's assessment of her working style. ''I'm used to people not expecting much from me,'' she said one afternoon late last month. ''But then as soon as I start working, that drops away. I don't yell. I'm petite. I don't turn into a tyrant. Being underestimated is, in a way, a kind of advantage, because people are usually pleasantly surprised by the result.''

Coppola was standing on a sound stage in the West Village about to direct a music video for the neo-garage-rock duo the White Stripes. She was looking even more adolescent than usual: her light brown hair was pulled back in a high ponytail, and she was wearing loose jeans, a blue-and-white-striped shirt and, to combat a chill, a too-large suit jacket that she borrowed from Lance Acord, her director of photography on the video. A few weeks earlier, Sofia had pitched the White Stripes' frontman, Jack White, her idea for the video, which was to be set to the band's cover version of Burt Bacharach's ''I Just Don't Know What to Do With Myself,'' from their recent album. ''I said, 'I don't know -- how about Kate Moss doing a pole dance?' '' Coppola recalled. ''I said that because I would like to see it. That's the way I work: I try to imagine what I would like to see.''

Coppola said this casually, a little like an aside, which is how she relays most of her ideas, big or small. She speaks softly, and her voice can trail off, even when she's paying close attention. While she does have strong opinions, she seems vague and shy, too vague and shy to be a director. Directors are supposed to be bold and forceful personalities: authoritarians. And yet, here she was, on a sound stage, talking calmly and quietly to her friends and me and especially to Kate Moss, the supermodel who was being asked to writhe suggestively with and along a metal pole in five-inch heels, black bra and ruffled bikini underwear. ''The band liked my idea,'' Coppola said, almost shrugging. Then she said: ''I have never tried to change my personality, to be more like my father. We approach things completely differently. He came on the set of 'The Virgin Suicides' and told me, 'You should say ''Action'' louder, more from your diaphragm.' I thought, O.K., you can go now.'' She laughed. ''I'm not going to say it wasn't intimidating, but when you direct is the only time you get to have the world exactly how you want it. My movies are very close to what I set out to do. And I'm superopinionated about what I do and don't like.'' She paused, and then she added, ''I may say it differently, but I still get what I want.''

Coppola is, in her way, puncturing the image of the excessive but singularly brilliant (male) director as omniscient genius, which was certainly reinforced by her father. She has inherited many of his talents -- his taste, his ability to surround himself with talented friends, his ambition and entrepreneurship. But she has her own way of making movies -- reflecting, perhaps, her being a woman. Interestingly, one of her father's professors at the U.C.L.A. Film School was Dorothy Arzner, the only major female director in the old Hollywood studio system. Her movies (including ''The Wild Party,'' starring Clara Bow in her first sound film, and ''Christopher Strong,'' with Katharine Hepburn as an Amelia Earhart-type pilot) revolved around the theme of strong women in a male-dominated society.

Hollywood was never a place where female directors thrived, and even in this supposedly post-feminist era, movies in America continue to be directed overwhelmingly by men. Nora Ephron has had box-office success (''You've Got Mail''); Amy Heckerling has had hits with ''Fast Times at Ridgemont High'' and ''Clueless''; and there has been a scattering of female-directed action films (by Mimi Leder, for instance, and Kathryn Bigelow) and indie films (Lisa Krueger's ''Manny and Lo,'' Mary Harron's ''I Shot Andy Warhol''). Still, in recent years, the most original and compelling films by female directors have been done outside America: think of Jane Campion (''The Piano'') and Gillian Armstrong (''My Brilliant Career''). The American movie industry continues to see its target audience as young men. Female directors are viewed as too soft, too personal, too limited in their visions -- too not one of the guys.

In a sense, by focusing ''Lost in Translation'' on a man having a midlife crisis -- and on Bill Murray, the actor who has cracked up millions of American men, first on ''Saturday Night Live'' and then in the movies -- Coppola has not made ''a woman's film.'' But in so many other ways she has, beginning with the very way she works. She doesn't demand but persuades, and she is open to change and improvisation -- in Murray's case, she simply asked him to fill in dialogue where he saw fit. What is hers is the vision, and the choices she makes as to the people who she believes can help her realize that vision. ''I'm not a girl, nor will I ever be,'' says Marc Jacobs, the clothing designer, who is one of Coppola's closer friends. ''But if I were a girl, I'd like to be Sofia. She's very feminine. And she's very quiet. But then, her movie's done. She loves fashion and music and art and film, and she is able to combine them in a way that all seems to be quite natural. There's nothing forced about it -- she doesn't have that gritty hunger to prove what she knows. There are certain people who have confidence and absolutely adore themselves and, five minutes around them, I just want to not be around them anymore. Sofia is confident in such a lovely way. It's not aggressive or arrogant, and that's a gift. I'm sure she works quite hard, but it all seems effortless.''

On the set of the video that day, Kate Moss was watching Robin Conrad, a professional choreographer who specializes in pole dancing, and a friend of a friend of Sofia's, as she slid up and down the metal pole ending in a modified back bend. ''Oh, I can do that,'' Moss joked, as she tried the same maneuver. Conrad, who studied dance at Cal Arts and has choreographed pole dances to Tom Waits songs, is a typical Sofia find. Conrad flew to New York a few days earlier and had been rehearsing with Moss since, downstairs at the Mercer Hotel in SoHo. (''There's a pole in the basement,'' Sofia explained.)

This is where the Coppola all-cool-worlds-collide element kicks in: most video directors aren't friends, the way Coppola is, with the owners of the Mercer. They haven't known Kate Moss since they were both teenagers, as Sofia has, and they don't pour champagne on the set from the family vineyard, which Coppola was doing now. The champagne, named Sofia, was created by her father, and the label reads, in part: ''revolutionary, petulant, reactionary, ebullient, fragrant, cold, cool.'' ''Her dad wrote that,'' said Zoe Cassavetes, Sofia's great friend, as she poured herself a glass.

Cassavetes -- the daughter of John Cassavetes, the groundbreaking director, and Gena Rowlands, his wife and a star in some of his best films -- met Sofia about 12 years ago, when they were both in a Vogue photo shoot. ''She was so quiet,'' Cassavetes recalled, ''that I thought she might be a jerk. My family lived at the Wyndham Hotel then. I grew up there -- Zsa Zsa lived on my floor. Sofia and her family were living up the street at the Sherry-Netherland. I said, 'Do you want to have dinner?' She said, 'O.K., do you want to go to Jean Lafitte?' -- which was a bistro on 58th Street, where I went all the time. When she said Jean Lafitte, we had an instant bond. We spoke the same language.''

After meeting Zoe, Sofia told her she was going to appear in a video for the Black Crowes, and Zoe ended up tagging along. They have been on sets together ever since. Around the same time -- the early 90's -- Cassavetes and Coppola met Marc Jacobs. Jacobs, in turn, had just met Kim Gordon and Thurston Moore of the seminal New York post-punk band Sonic Youth. They, in turn, were working with Spike Jonze, who was shooting skateboard footage for a music video of theirs. There was lots of hanging out, Jonze met Coppola and the rest is history: Coppola had found her network and her husband (she and Jonze married in 1999), who would become, with ''Being John Malkovich'' and then ''Adaptation,'' a celebrated young director himself (with some help along the way from the Coppola family and network). ''My first impression of Sofia,'' Jonze recalled recently, ''was that she was quiet and graceful. And that she had taste, and when I say taste, I mean judgment in really subtle things. She always knew the feeling she wanted to convey in everything she did. And that's true taste.''

The extended Coppola clan likes to work together. A couple of years after their marriage, Jonze cast Sofia's cousin, Nicolas Cage, in ''Adaptation.'' A few years earlier, Sofia had suggested another cousin, Jason Schwartzman, for the leading role in Wes Anderson's film ''Rushmore.'' In turn, Anderson helped Sofia get Bill Murray for ''Lost in Translation.'' And so it goes, like a chain letter you are happy to receive.

''That's the dynamic of the Coppolas,'' explained Anderson, when I reached him by phone near Rome, where he is filming his next movie. ''They collect interesting people. They have a leader in Francis who cooks up things to do together. They work on each other's projects, and they like to add members to the family. Francis has been doing that since the beginning of his career. He's always liked the idea of an extended family -- his extended family were people like George Lucas and Martin Scorsese.''

Cassavetes made much the same point as she sipped her champagne on the video set. ''You have to be introduced to things in life,'' she said, as Sofia and Jack White studied the black-and-white image of Kate Moss on a replay monitor. ''Sofia's parents introduced her to so much and to so many people. It's understandable that she would continue that tradition. The more important thing to understand is that her family advocated work. Francis would have them work on his movies and direct plays in Napa. It is, after all, the family business.''

Coppola was conferring now with Moss, telling her to snake up the pole a little more slowly. Moss, who turned down a short white robe offered by an assistant, was remarkably comfortable in her underwear and sat with her feet up in front of a fan. ''My body has not had this much exercise in its whole life,'' she said.

While she rested, Sofia planned the next shot. ''I think the camera is too close to her behind,'' Sofia almost whispered to Acord, the cinematographer. She perched next to him. It was one of those moments when being a female director probably makes a difference. What male director wouldn't have had his camera relish close-ups of Moss's near-naked body? ''I'm self-conscious about that shot,'' Sofia said quietly. ''I know we're making a sexy video, but it's sort of brave not to show too much. We want it to be a little Fosse, but I also want it to have that weird Factory feel.''

As it is with Coppola, the hot-wiring of disparate cultural references -- Broadway jazz choreography mixed with the grainy, improvisational feel of Warhol plus Kate Moss and a bluesy version of a classic Bacharach song sung by Dusty Springfield -- resulted in something original. ''You have to be Sofia to make this work,'' Cassavetes said as she watched Moss dance on the pole. ''If you're not Sofia, it's too obvious, too self-conscious or just, somehow, not quite there. Unless you're Sofia, the elements don't mesh. Where other people get stuck on a trend or a look, she can create a world.''

Sofia Coppola more or less grew up on film sets. She was born in May 1971 during the making of ''The Godfather,'' and in the christening that is part of the movie's final, climactic scene, she is the baby. When I asked Francis Ford Coppola about this, via e-mail, he said: ''At the very beginning of my own career, I had resolved that I would never travel to any location without taking my kids along. Although it makes academic skills suffer, it compensates with a sense of the world cultures beyond one's own. And, of course, hanging around and participating in the various movies gave them experiences that would be tough to come by any other way.''

Sofia recounts her childhood according to the movie her father was shooting at the time. Oh, that was when we were in L.A. during ''One From the Heart,'' she'll say. Or that was during ''The Outsiders'' and ''Rumble Fish,'' when we lived in Oklahoma. She got to know New York when her father was shooting ''The Cotton Club'' in 1983. And despite all the famous problems on and off the set during the making of ''Apocalypse Now,'' some of her happiest memories were when she was 6 and her father was directing that film in the Philippines. ''I loved the helicopters,'' she recalled. ''There were big dramas, but, as kids, our life never really changed. My father was always involved with us, and we were sheltered from a lot of what was going on elsewhere. Being the only girl in the whole family, including my cousins, meant that I was particularly sheltered. I'm sure that affected my personality. I'm the only girl and the youngest in an Italian family -- I will admit that they fussed over me.''

Her father regularly cast her and her brothers in small parts in his films. ''When I was 10,'' she recalled, ''I took the stage name Domino. As Domino, I played Diane Lane's bratty little sister in 'Rumble Fish.' My father just wanted to have his version of home movies.'' In 1989, when she was 18 and had graduated from high school in Napa Valley, Sofia was asked by her father to replace Winona Ryder in ''Godfather III.'' ''The part was written somewhat based on Sofia,'' Francis Coppola recalled, ''and so in order to prevent what I felt was an unnecessary delay as well as casting an actress I felt was wrong for the part, I put Sofia in the movie.''

Her portrayal of Mary Corleone was widely attacked and ridiculed. ''The critics tore me apart,'' Sofia told me. ''But I didn't want to be an actress. If I had, then it would have been harder.'' Her friends claim that the experience left Sofia wary. ''Can you imagine?'' Cassavetes told me. ''The press did the same thing to Anjelica Huston when her father first directed her. It wasn't until he directed her again in 'Prizzi's Honor,' which was about 15 years later, that they took her seriously. Sofia didn't deserve to be blasted like that. Plenty of performances don't work -- the critics were brutal to her.''

Coppola's friends' protectiveness about her can be attributed, perhaps, to her experience with ''Godfather III.'' Clearly, she is a willful and persistent young woman underneath her seemingly fragile exterior. Still, those close to her are very careful about pushing her too far or even asking too many questions. ''I think Sofia unknowingly inspires that protectiveness,'' Wes Anderson says. ''You want to help her. You want to look out for her. She turns everyone into her big brother.''

After ''Godfather III,'' a failure not only for her but also for her father, Sofia avoided the movie business. ''I became a dilettante,'' she admitted. ''I wanted to do something creative, but I didn't know what it would be.'' At the urging of her mother, Eleanor -- a documentary filmmaker with a keen interest in the visual arts -- Sofia attended Cal Arts but eventually dropped out. She studied photography -- again, at her mother's suggestion, Eleanor having given her as gifts pictures by William Klein and others. Briefly, Sofia had a TV show on Comedy Central with Zoe Cassavetes called Hi-Octane, in which they mostly drove around L.A. in a vintage GTO and interviewed their friends. In 1995, she created a clothing company called Milk Fed with Stephanie Hayman, her oldest friend from grade school in Napa Valley. (The Coppolas have always kept the house there as their home base, where they also have a vineyard. Between Francis's movies, they would usually return there.) ''Sofia was always fashionable,'' Hayman recalled. ''I think she had things from Chanel in seventh grade. When I moved to L.A. from Napa, we talked about making some clothes. We're both very petite and have trouble finding things in our size. So we started Milk Fed. The company just took off. Now, we do four collections a year, and we make everything from underwear to overcoats. ''

Although Coppola has less and less to do with Milk Fed, it is lucrative. ''The clothing company does well enough that I don't have to make money from movies,'' she says.

Milk Fed is now sold almost exclusively in Japan, where the clothes are produced and where the company has a store called Heaven 27. When they are in Tokyo, Sofia and Stephanie always stay at the Park Hyatt hotel, where ''Lost in Translation'' is set. ''They let us film there because I've stayed at the hotel,'' Sofia explained. Yet another connection made.

In 1995, Thurston Moore (of Sonic Youth) gave Coppola a copy of ''The Virgin Suicides,'' the first novel by Jeffrey Eugenides. It's set in the 70's in Grosse Pointe, the Detroit suburb, and tells the story of the beautiful, tragic Lisbon sisters. ''I loved how the book talked about something gone,'' Sofia said, ''whether it's an era or a person or innocence. I felt like Eugenides understood that feeling.'' Francis Coppola has said that he believes Sofia's deep attraction to ''The Virgin Suicides'' was related to the death, in a boating accident at age 23, of her oldest brother, Gian-Carlo, known as Gio. ''Gio was that kind of enchanting older brother who would take me on adventures and treat me like an adult,'' Sofia recalled. ''Gio and my other brother, Roman, did everything together. I was in Napa with my mother when Gio died. It was a heartbreaking time. You never really get over something like that.'' Sofia paused, then went on to say: ''I think some of that sadness went into 'The Virgin Suicides.' I think I'm always drawn to projects that help me understand something about myself.''

Sofia began adapting the book for the screen even before she secured the rights to it. She worked slowly. She based the look of the Lisbon sisters on Stephanie Hayman's younger sister, Leslie, whom Sofia saw as cool, blond and every suburban teenage boy's dream, and after the script was done, she cast Leslie as one of the sisters. The look and feel of ''The Virgin Suicides'' was inspired not by other films or even the setting (it was actually filmed in Toronto) of the movie but by contemporary art photography: the pictures of William Eggleston, Tina Barney, Bill Owens and others. ''It was the beauty of banal details that was inspirational,'' Coppola explained.

While writing the script, Sofia contacted Julie Costanzo, an executive at her father's company, American Zoetrope; Costanzo tracked down the filmmakers who already held the rights to ''The Virgin Suicides.'' After reading Sofia's script, they junked their adaptation and gave her the project. She cast the child actress Kirsten Dunst, who was most famous for passionately kissing Brad Pitt in ''Interview With a Vampire,'' in her first ''adult'' role and gave Josh Hartnett his first major part. ''The Virgin Suicides'' is a shimmering paean to adolescent obsession and desire, seduction and abandonment, innocence and its destruction. Here, as she is in ''Lost in Translation,'' Coppola is fascinated by memory, by moments -- good and bad -- that will never be forgotten, moments at the center of which are young women on the verge of something they cannot quite articulate but feel compelled to act upon. It's these particular moments Coppola has captured on film so beautifully and movingly.

One sunny July afternoon in Hollywood, Coppola pulled up in her dark blue Porsche at the Directors Bureau, the company that her brother, Roman, who is six years older than she is, co-owns. She and Spike Jonze live nearby, in a stone-and-stucco midcentury house in the hills of Los Feliz. Until recently, she drove a Cadillac (''my Mafia princess car''); the Porsche is a new toy. She opened the car door and tugged at her keys, which were stuck in the ignition. ''I'm having a midlife crisis,'' she said, alluding to a scene in ''Lost in Translation.'' ''I bought a Porsche.'' She pulled at the keys, twisting them right and left. ''I can't get them out,'' Sofia said, smoothing her short black skirt. ''I'm going to go get Roman. That's why I have a big brother.''

At the Directors Bureau, Roman Coppola has spent most of his time channeling the late 60's. His feature film ''CQ'' was an homage to all things cool in 1969 (from the vantage point of the year 2000). Roman also has directed videos for fellow aficionados of time tripping -- bands like the Strokes and, his new favorite, Phoenix, a French pop group whose music is featured in ''Lost in Translation.'' On this day, Roman was blowing up a large plastic pillow in the ground-floor lobby of the Directors Bureau. He made the pillow, which resembled a six-foot bubble, out of clear garbage bags, from ''Inflatacookbook,'' created by the 60's art collective Ant Farm. ''They built these for happenings and whatnots,'' Roman said as he inflated the pillow with a fan. ''We're applying this pillow for another purpose.''

Roman was constructing the plastic bubble for a Toyota Prius commercial that he would be shooting the next week. This was before he was flying off to Monte Carlo to play roulette, but that's another story. ''It was a bit of a eureka moment when we thought of the pillow,'' Roman said to Sofia.

Now Sofia's friend Brian Reitzell arrived, with the first CD's of the ''Lost in Translation'' soundtrack. Reitzell plays drums with the French electronic group Air, which Sofia had tapped to compose the soundtrack for ''The Virgin Suicides.'' Reitzell himself put together the soundtrack for ''Lost in Translation,'' coaxing the reclusive Kevin Shields, founder of the seminal group My Bloody Valentine, out of seclusion. Reitzell is also the boyfriend of Stephanie Hayman, Sofia's good friend and partner in Milk Fed.

''What is that?'' Sofia asked, as the bubble inflated. ''We needed a white environment to surround the car,'' Roman explained. ''The bubble allows the lights to be on the outside. That way, the car has no reflections on it. Roman paused. ''Get inside,'' he said. ''We're getting a patent on this. We're going into the pillow-making business.''

Sofia and Reitzell stepped into the bubble, which had expanded to fill the entry and blocked off the front door to the Directors Bureau. The bubble business is not Roman's only sideline. ''Entrepreneurship is a family disease,'' he explained. ''My father has a magazine, a food business, a wine business. In the early 80's, there was an article about Belize, a little country that had a revolution. And my Dad and Gio went to check it out. Then we started going there. Now he has a resort called Turtle Inn in Belize.'' Roman has his own wine, RC Reserve, which is a syrah blend. He's a partner in a beauty line, Uvavita, that turns grape-seed extract into age-defying potions. And now he's a bubble designer.

Everyone in the Sofia-orbit has side projects. Her husband Spike Jonze has two skateboard companies that also make clothes. This summer, Sofia designed some canvas bags for Marc by Marc Jacobs, his lower-priced line, and, two years ago, she inspired the scent of his perfume and appeared in the ads for it. ''It was fun to be a perfume girl,'' she said. ''I was true to my scent.'' She is currently talking about flying to Rome to film a documentary about Wes Anderson's learning Italian on the set of his new movie. Marc Jacobs told me, ''In this crowd, if you don't have at least two careers, you don't fit in.''

Sofia sat down on the pillow's floor. ''It's nice in here,'' she said, her bare legs at her side, ankles neatly crossed. Roman's cellphone rang. ''Hi, Dad,'' he said. ''We're in the pillow.'' Pause. ''Yes, it works.'' Pause. He handed the phone to Sofia. ''My jet-set father,'' she said, hanging up. ''He's off to the jungle for the rest of the month.''

After they emerged from the bubble, Sofia and Reitzell decided to walk down the alley to the Sound Factory, where Phoenix was recording. ''This is a fun field trip,'' she said to Reitzell. At the Sound Factory, Phoenix, which has that Euro meets preppy look that characterized the early Stones, are standing around a recording console, going over their lyrics in English. ''When I heard your first record, it blew my mind,'' said Reitzell, whom they know from his work with Air. ''We're trying to make you famous,'' Sofia said.

The band plays their latest track. It was an infectious pop song. Sofia leaned back in her chair at the console, surrounded by seven boys. ''That song makes you want to be in love,'' she said. ''Let's hear it again.'' The song played. ''I'm right at home,'' Sofia said. She had found new members of the family.

''Lost In Translation,'' which slowly unspools the story of a middle-aged American actor on the downslope and a woman just out of college who meet when both are staying at the Park Hyatt in Tokyo, was written by Coppola specifically for Bill Murray. ''I always wanted to work with him,'' Coppola said one afternoon in New York. She was sipping iced tea at Il Buco, in the East Village, which is not far from her Manhattan apartment. She spent most of the spring in New York, editing ''Lost in Translation'' in SoHo. ''I didn't want to edit this movie in L.A.,'' she said. ''I wanted to see people on the street, to walk to work. That was the feel of the movie, and I didn't want to lose that mood.''

Initially, with ''Lost in Translation,'' Sofia wrote a kind of short story instead of a script, and the film retains that loose, lyrical feel. The plot is minimal: an American movie star named Bob Harris arrives in Tokyo to film a commercial for a Japanese whiskey. His sense of midlife dislocation is matched by the 20-something driftiness of Charlotte, an equally jet-lagged and sleep-deprived woman who winds up seated next to him late one evening in the hotel bar. When her husband, a self-involved fashion photographer, gets an opportunity to go off for a few days to shoot a rock band, he takes it, leaving his young wife to fend for herself. Bob and Charlotte strike up an unlikely alliance.

The relationship of the fashion photographer and his young wife may or may not have shadings of Coppola's own life and her relationship to Jonze. Giovanni Ribisi, who plays the photographer, speaks with Jonze's mannerisms, and Scarlett Johansson, as Charlotte, is dressed and styled to seem a lot like Coppola. ''I know,'' Coppola says, ''how narcissistic.''

In the last few months, Jonze and Coppola have been distant, rarely living in the same city. ''It's been rough being apart so much,'' she explained. ''But we have to figure out our relationship after Sept. 12, when the movie comes out.''

''Lost in Translation'' was easy to cast. Coppola right off wanted Johansson, who is only 18 but has been acting since she was 8, and Johansson said yes immediately. But Bill Murray, who was crucial to the success of ''Lost in Translation,'' was, as he always is, elusive. Coppola was friendly with Mitch Glazer, a screenwriter who is one of Murray's best friends. She showed him her 10-page treatment and asked for help. ''Sofia is amazing because she's such an artist, but she grew up in a family that gets things done,'' Glazer said. ''She knows how to be relentless. She's completely genuine, but she is as driven and tough as anyone I've met in Hollywood. And she wanted Bill. She had written it for him. When she was pursuing Bill, I talked to her more than I talked to my wife. She talked to me a thousand times. In that sweet way, but persistent. In more than 20 years of friendship, I never said anything was perfect for Bill, and this time, I did. But Bill is difficult. He wouldn't give anyone an answer.''

Without Murray, Coppola knew that the movie wouldn't capture the mix of humor and sadness she was after. ''People said, 'You need to have a backup plan,' and I said, 'I'm not going to make the movie if Bill doesn't do it,' '' she recounted to me. ''Bill has an 800-number, and I left messages. This went on for five months. Stalking Bill became my life's work.''

Wes Anderson was enlisted. ''I was lobbying for Sofia,'' he recalled. Then, one day in mid-July last year, Murray, Glazer and his wife, the actress Kelly Lynch, were having lunch at Il Cantinori in New York. Glazer invited Coppola, who was in town, to join them. ''She was so adorable,'' Glazer recalled. ''And, like any man, Bill appreciates a worshipful audience. When I saw them together, I realized it was done -- he'd do the movie.'' The next night, Anderson joined Sofia and Bill at another restaurant. ''It was one of those patented Bill evenings. He was driving. He went through a red light, reversed the car and then ducked into this Japanese place that only he could see. By the time the sake came, I knew he would do the movie.''

The pursuit of Bill Murray is typical of Sofia's directorial style. If she's not going to hit the note perfectly, she'd rather not hit the note at all. ''Sofia has such a strong point of view,'' Jonze said. ''And, really, that's what being a director is: knowing what you would like and what you don't like and standing by that, despite all the pressures.''

And yet, even after committing to ''Lost in Translation,'' Murray was worried. ''The whole thing felt slight, which was a little troubling,'' he said. ''But she had a way of saying her dream wouldn't have come true unless I did the movie.'' He smiled. ''I got reeled in from way, way offshore, but Sofia's very good on the phone, and she spent a lot of time getting me to be the guy. In the end, I felt I couldn't let her down. You can't ruin somebody's dream.'' Murray didn't dwell on Sofia's sex. But Scarlett Johansson, who has the ripe looks and sensitive manner of Sofia herself, says working for Coppola is different from working for men. ''It's like the difference between a female teacher and a male teacher,'' she said. ''In the first scene in the movie, I am photographed from the back in sheer pink underwear. Now, I'm not a really physically fit type of person, and I was afraid to wear the underwear. Sofia said: 'I'm going to try on the underwear and show you what it looks like. Then, if you don't want to do it, you don't have to.' Well, I've been directed by Robert Redford, who is very handsome, but I can't imagine him suggesting that. Only a female director could get me to wear the underwear. And we shot it.''

''Lost in Translation'' cost less than $4 million and was filmed in just 27 days. Coppola worked the cast and crew hard, but also let people do what they are good at, figuring she could edit what they had chosen to do later. She suggested, and she was happy to be surprised. Having spent so much of her life on movie sets, she easily created a familial environment. Her friends were always nearby, working, talking, listening. Interestingly, and perhaps tellingly, she told very few people beyond those working with her that she was off shooting. ''It was a stealth production,'' she told me as she dropped ice into her tea. ''I didn't really want anyone to know about it. I know a guy would have done things differently, and there are times I had that personality.'' She paused and then smiled. ''But not very often.''

During the 4 p.m. lunch break for the White Stripes video (they'd started at 1), a long table was set up in the empty garage of the studio. It was a beautiful afternoon, and an assistant opened the garage door onto West 12th Street. ''This is why I didn't want to shoot in Queens,'' Sofia said, as she surveyed the street in all its Greenwich Village charm. As it often does in Sofia's life, the scene outside fit perfectly with the video scene inside. The real-world mood -- a kind of polished bohemianism, full of interest -- and the movie mood matched, which is Sofia's way.

This day, and most days, she had carefully chosen all aspects of her life, detail by detail, in what appeared to be an effortless manner. ''Sofia knows how to create a great environment,'' Bill Murray said. '' 'Lost in Translation' was a very difficult shoot. The jet lag in Tokyo was so bad that when we had to film the actual jet lag stuff in the movie, I was out for two and a half hours. Sofia is attentive to the smallest nuances. She knew when she had it and when she didn't. And that can be very hard to tell with subtle material. But it's why we're here.''

Although the video production had brought in a food truck to cook lunch, Sofia ordered sandwiches from Tea and Sympathy, a restaurant that specializes in British food. This was for Kate Moss. And for ambience. The cucumber-and-egg-salad sandwiches, with their crusts neatly removed, set the tone Sofia sought.

''I'm always thinking,'' said Zoe Cassavetes, as she surveyed the platter of sandwiches, which had been placed next to a bottle of Sofia champagne, ''I must take lessons from Sofia. I've been on sets as long as she has -- my father made 75 percent of his movies in our home -- and I don't know how to create atmosphere like Sofia. On location, she has her candles everywhere, and she puts up pictures of her friends and family, pictures that inspired the movie, and she puts them up with that good artistic tape. I travel a lot, and I don't do that. But that's just the way she is. You can see it in her work. Everything can be going mad around her, and she'll sit and have a glass of wine, and then she'll go back to being totally focused. She leans in and says something to an actor -- some small, key detail only she would notice -- and she gets exactly what she needs.''

Cassavetes, who says she hopes to direct her first film this fall, sat down. She has a distinctive face that would work perfectly in an Italian movie from the 60's, and she was wearing a short skirt. ''I'm very, very protective of Sofia,'' she continued, as Kate Moss and her makeup artist emerged from the sound stage. ''She inspires that. You want to protect her. She sees the world a certain way, and I don't want the world to let her down.''

Cassavetes lighted a cigarette. ''What lovely sandwiches,'' Kate Moss said. Sofia smiled. Moss had changed into jeans and a loose chiffon top. She showed Coppola, who sat down across from Cassavetes, some photos of her 10-month-old baby girl. ''She looks like her father,'' Moss said. The father is Jefferson Hack, the London-based editor of Dazed and Confused, a hipster magazine. Sofia has worked for the magazine; two weeks ago, she sent Hack a photo she took of Kirsten Dunst at the Costume Institute gala at the Metropolitan Museum. Coppola's date that night was Marc Jacobs. As usual, the dots connect in a particularly spectacular way.

Jack White, who was dressed all in black except for a white splint that protected a broken finger, sat at the end of the table. Earlier, Sofia asked his partner, Meg White, who, like her bandmate, sticks at all times to the White Stripes' color scheme -- black, white and red clothing -- if she had seen the Elizabeth Peyton portrait of Meg. Sofia asked this sweetly, but as her worlds usually collide, she fully expected Meg White to know Elizabeth Peyton's work. ''It's such a good painting, and she didn't even know about it,'' Sofia said, somewhat incredulous. ''I will have to send you a print of it, or something,'' she said to Jack White. He nodded and reached for a sandwich. ''We'll get Meg up on the pole after lunch,'' he said.

Moss and Cassavetes both lighted another cigarette. ''I just started smoking again,'' Cassavetes said. The conversation turned to cigarettes in movies. ''No one ever looked cooler smoking than my dad,'' Cassavetes said. Moss agreed. ''Your dad was really cool,'' she said. It's a striking moment: a rock star, the top fashion model in the world and the children of two men who changed modern cinema were chatting over tea sandwiches. The quietest one at the table was Sofia, and yet, she was the motor that powered this scene. She looked serene, contemplative. ''My dad always said,'' Cassavetes continued, ''to do one creative thing every day. Whatever it is.'' Moss dragged on her cigarette. ''I think Sofia grew up with the same imperative.'' Sofia smiled. It was time to get back to work.

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