“Quantico,” a new crime drama debuting Sunday night on ABC, is one of those pulse-racing serials that flashes back and flashes forward, and you’re never sure if anyone is really telling the whole truth. With hundreds of scripted shows this fall season, several of them with that familiar premise, why should audiences watch this one?  “Besides the fact that it’s one of the most diverse casts I’ve ever seen on television?” asks its star, Priyanka Chopra, 33. She plays an FBI trainee who becomes the agency’s top suspect in a deadly terrorist attack. And, she argues, in this show, “everyone’s breaking the stereotype of what they should be.”  “Plus,” she adds, “it’s super entertaining.”  Chopra is correct on all counts. “Quantico,” which has received some of the better reviews of the fall season, was created as the highly anticipated U.S. television debut of a woman who is one of Bollywood’s biggest stars. She was the first actress cast after the head of ABC’s diversity talent casting program — the same executive who discovered Oscar winner Lupita Nyong’o — flew to Chopra’s home in India last year, persuading her to sign a talent holding deal with the network.  [Review: ‘Quantico’ doesn’t mess around]  Chopra — a model, singer and former Miss World who has starred in dozens of Bollywood films — was initially skeptical of the time commitment, as well as the types of parts that she would be offered. Eventually, she agreed to fly to Los Angeles for pilot season. The script for “Quantico” caught her attention, particularly the character of Alex Parrish.  Alex is the focus of the pilot episode, as one of the FBI’s brilliant new recruits enduring a physically and mentally grueling boot camp. She’s tough, complex and fiercely independent, a la “Homeland’s” Carrie Mathison — equipped with the requisite tragic back story, and game to hook up with the random guy she met on the plane on the condition that it only be a one-time thing. (Spoiler alert: He turns out to be a fellow FBI trainee.) Things take a scary turn when the action flashes forward several months to the aftermath of massive terrorist attack at Grand Central Station, for which the FBI suspects one of its new recruits.  “I always choose my scripts based on things I want to watch. It’s a really compelling story,” Chopra says by phone from the set in Montreal. (The show also films in New York.) “And Alex is an amazing girl. I wish I had the balls to be like her. She’s bold and empowered, and she knows what she wants. . . . She’s today’s modern-day global woman. She has flaws, and she embraces her flaws.”  An FBI drama also appealed to Chopra, known for starring in Bollywood action thrillers. Her global celebrity status created one of the sticking points in signing on to “Quantico”: She insisted the show be available to her fans worldwide, especially in her native India. At recent count, she has 11 million Twitter followers, 3 million on Instagram and nearly 17 million on Facebook.  “For me, that was very important,” Chopra says, who recently filmed commercials in Hindi for the show, which will air in India next month — faster than the typical delay of six months or a year for an overseas series.  After her initial hesitance about the workload, Chopra says she is indeed exhausted by the breakneck pace and 15-hour days of a broadcast filming schedule. She admits she wasn’t quite prepared for it but says she loves it.  And the big differences between an ABC drama and a Bollywood thriller?  “On set, it’s pretty much the same,” she laughs — directors and actors and crew members stumbling over each other, everyone “going crazy” hitting their marks on time. “It’s the same chaos everywhere.”  Emily Yahr covers pop culture and entertainment for the Post. Follow her on Twitter
The FBI drama — she plays a recruit-turned-terror-suspect — has some of the best reviews of the season.