This question is very similar to one that I have answered recently, so here goes. Women have some very key roles in this excellent novel. Whilst the main focus of this novel is postcolonialism and in particular the fragile and transitory status of boundaries and frontiers, a key concept within postcolonial studies is how gender impacts on this topic. It is particularly interesting how two characters, the narrator's grandmother Tha'mma, and his cousin Ila, impact the theme of the novel, in particular with their attitudes towards nationalism.
Tha'mma epitomises the views of the Nationalist movement and India's nationalist identity. She has a passionate and blind love for her nation, even though she is a migrant from Dhaka and therefore not strictly Indian - of course, this is a key concept in postcolonialism, how the "Imagined Communities" of nations are formed and how belonging is defined. Tha'mma, when filling in an official form writes her nationality without question as Indian, but then has to state her place of birth, which was in East Pakistan. This causes her to question her national identity and how it is formed.
Tha'mma's return to Dhaka, her birth town, raises other interesting themes extremely pertinent to postcolonialism, and that is the concept of "home" and how it changes through an act of leaving your home. Tha'mma searches for what she calls the "old Dhaka", as she finds Dhaka, her original "home", a very alien place. She is told, "But you are a foreigner now". The act of migration changes concepts of "home" and "belonging" forever.
Her blind belief in India is mocked and questioned by other characters. The narrator's father mocks her saying: "did she really think the border was a long black line with green on one side and scarlet on the other, like it was in a school Atlas?". She is unable to conceive the fractual reality of borders and on her return to Dhaka donates her prized possession - a ruby necklace - to the "war effort" - to support Indian troops.
If blind attachment to the concept of nationhood is reflected in Tha'mma, Ila reflects Western disregard for third-world histories and the "aproved" take on history. Ila tells her cousin that "nothing really important happens where you are" and feels that the political revolutions in the West are far more important than famines and other natural disasters suffered by nations. Of course, Ila does also reflect the constraint placed upon women, for example when she is forced out of a cabaret bar by her uncle. This reflects how gender inequalities still exist, even in a time of "post-colonialism", and how they can be reinforced by male patriarchy.