Sounds like Primary Inversion, by Catherine Asaro. I think there was something about the alien race being related to Incan or Mayan people. It is the first book in the Saga of the Skolian Empire series.
The Skolian Empire rules a third of the civilized galaxy through its mastery of faster-than-light communication. But war with the rival empire of the Traders seems imminent, a war that can only lead to slavery for the Skolians or the destruction of both sides. Destructive skirmishes have already occurred. A desperate attempt must be made to avert total disaster.
The plot elements are most likely from the second written novel in the series, Catch the Lightning:
The first half of Catch the Lightning takes place in an alternate Los Angeles on Earth in a time similar to the late 20th century. The main character is Tina Pulivok, a seventeen-year-old Maya girl living in East L.A. She has relocated to Los Angeles and is living on her own while she works as a waitress. The hero, Althor Selei, a cybernetically enhanced Jag fighter pilot, is thrown into the alternate universe when his star fighter malfunctions. Tina meets Althor late at night when she is returning home from work, and he is trying to figure out why he ended up on a planet that bears little resemblance to the Earth he expected. After Althor helps Tina escape an incident of gang violence, the two become fugitives.