On any given day, Diane Kruger rides a cream-colored Vespa around Los Angeles. She buys white wine in Los Feliz or sees action movies—recently Pacific Rim—at the ArcLight in Hollywood. If you surf onto enough gossip websites, it’s easy to follow the 37-year-old German-born model and actress performing any number of quotidian tasks. What’s a lot more interesting to watch, though, is The Bridge. That’s Kruger’s new FX series (based on the Scandinavian show Bron), and beyond being a compelling nail-biter, it’s a weekly showcase for how remarkable Kruger can be when she’s not just being herself.

On The Bridge, Kruger plays Sonya Cross, an El Paso, Texas, cop attempting to solve a crime that left halves of two bodies placed together on the bridge that connects the United States to Mexico. These are the first of many murders in a case that involves race relations, immigration and class issues; complicating the matter is Marco Ruiz, Demián Bichir’s good-natured Mexican cop intent on being part of the investigation.

On top of it all, Kruger’s character suffers from Asperger’s syndrome, making her awkward in social situations, difficult to work with and exceptionally interesting to watch while she tracks a killer. “It’s a continuous challenge to make her real,” Kruger says, “to portray someone who has the condition but who is exceptionally good at what she does.” Still, Kruger wasn’t immediately sold on playing Cross.

As Elwood Reid, one of the show’s creators, remembers, “I sent Diane the script and I didn’t have a back-up plan. It was a scary thing because she was the first person we went to. She said, ‘I’m interested. But I think the character’s kind of a bitch.'”

One meeting and a few rewrites later, Kruger was on board. Not only had Reid agreed to develop the character’s backstory, but the actress was charmed by the medium. “I love that people will invest time into [TV] shows and you don’t have to be this likeable character from the get-go,” Kruger explains. “What is interesting to me is showing a complete picture of a very humane person.”

While Kruger’s never had a series to herself before—you likely know her from films such as Inglourious Basterds and The Host—she does have a seasoned adviser in her longtime boyfriend, Joshua Jackson, a veteran of Dawson’s Creek and Fringe. Surely he offered guidance for her cable debut.

“He was actually very jealous,” Kruger says with a laugh. “He was on a network sitcom, so his days were crazy long. A regular day would be 14 or 15 hours of shooting. Now, I’ve been home for dinner pretty much every night since we started the show, so he’s just a tad envious.”

Not only is she home early, but Kruger’s been taking the job home with her as well.

“Demián and I have become very close; he’s one of the major reasons I wanted to be part of this,” she says. “We have a fun time on set together and in our personal lives. Our significant others are both Canadian, so we spend a lot of private time together.”

Bichir, the Oscar-nominated Mexico City native best known for playing a crooked Tijuana mayor on Weeds, admits the admiration is mutual. “Diane shows so much depth and grace,” Bichir says. But lest we think Kruger’s all work all the time, he adds, “I think she is 30 percent German and 70 percent Mexican, but she just doesn’t know it yet. She has the same sense of humor as us. She would be great doing comedy.”

In fact, there’s not much Kruger can’t do. In addition to her acting career—now flourishing here but already strongly established overseas—she’s a beauty-campaign mainstay, lending her visage to companies like Lancôme and Chanel, the latter, of course, run by her longtime friend Karl Lagerfeld.

“Karl Lagerfeld’s my neighbor in Paris; I’ve known him since I was 16,” she says. “He never sleeps, he prefers to work at night, so when I come home from work, I often see him in my street. They often shoot outside, and I get sucked into having a drink, and then, there you are, it’s four o’clock in the morning and you’re still talking.”

While she’s in L.A., however, it’s Sonya Cross who seems to monopolize her time. The Bridge launched to a respectable 3 million viewers and, thanks to DVR viewing, became FX’s third-biggest premiere ever. So, while the first season is still filming, hopes are high it will be renewed for a second. This early success is a testament to Cross, one of the most multilayered characters on TV, and the talented actress who plays her.

“I wouldn’t have signed on to the show if she were a regular hard-ass cop,” Kruger says. “I’m fascinated by women who appear to be one thing and then really are not.”