It would be very appropriate to analyze this novel through the idea of hybridity, both in postcolonial India and its application to the Indian characters in the United States. Homi Bhabha's ideas about the ongoing impact of relations between colonizer and colonized, especially through selective adaptation or "mimicry," extends into the ongoing impact on the subsequent generations after official colonial rule ends. That is the situation for Desai's characters, as British rule of India ended in the 1940s.
The imposition of the dominant nation's ideas about superiority, including race and culture, results in uneven acceptance by the colonized. Struggles over identity, including alienation, result as they emulate the ways of the foreigners who disparage them.
While the novel as a whole shows the postcolonial legacy, or inheritance, of hybrid identity issues, an effective thesis might focus on the ways these play out in specific characters, such as:
Biju and Sai, in their differing U.S. and Indian settings; or Sai and the Judge, indifferent generations.