Can Rebekka Bay Fix the Gap?

Rebekka Bay, the creative director of Gap, has strict rules about how to design a collection. She also has rules for how to break the rules. “Fashion is also about instinct and gut reaction,” she says. “So if I suddenly wake up in the middle of the night and think, ‘The shirt has to be frilly,’ and that’s what we really want, then I’m going to say, ‘Of course it has to be frilly.’ ” The frilly shirt will be in stores this fall.

Bay is a 44-year-old Danish fashion designer who had never worked in America until October 2012, when she joined Gap, the once-celebrated brand that had been disappointing Americans for years. She had, though, studied the American uniform of khakis and jeans that Gap helped define. On a recent winter day she has on black Gap jeans (which will be available later this year) and a simple, navy blue Gap sweater (also available later this year). Her only jewelry is a gold wedding band; if she’s wearing makeup, it’s barely discernible. “I am happiest if I have jeans in a couple of washes, tees in black, white, and heather gray, and a seasonal coat to pull off the look.”