How is the theme of gender identity portrayed in Puig's Kiss of the Spider Woman?

In Kiss of the Spider Woman, Puig portrays gender identity with the rich but painful irony that our desire to define it in our own terms may confine us much as liberate us. The confinement that results is concrete and overt as both Molina and Valentin are thrown in prison: Molina for daring to define herself as a woman by having sex with men and Valentin for daring to define manhood as commitment to Marxism.

The irony strikes when they are thrown together.

With her stories and unrepentant fantasies, Molina forces Valentin to question how rigidly he has defined what it means to be a man. Must a real man hide his feelings? Must he always commit to reality and never indulge in storytelling or fantasy?

With his relentless interruptions and “male logic,” Valentin forces Molina to question how rigidly she has defined what it means to be a homosexual. Does loving a man mean you have to identify as a woman? Is prison the only place she can really be free?

Even in chapter 14, when Molina is released on parole and attempts to deliver a message for Valentin, and Valentin takes refuge in fantasy while he is being tortured, the trade-offs in liberation and confinement remain mixed and painful. Valentin has become liberated enough to initiate sex with Molina, but does he do that only as a masculine sacrifice? Molina has become liberated enough to take on the “macho” role of messenger, but does she do that only to prove to Valentin that she is an ideal woman? Puig refuses to resolve these questions for the reader, and that is precisely what makes this novel so successful and powerful.

I think that gender identity is portrayed as something that can be malleable.  The way in which one sees themselves in terms of their gender association is not something entirely fixed.  It is not static.  Consider that Molina's real name is "Molino."  His movement of the "-a" at the end of his name at the cost of the "-o"is reflective of a gender switch, moving to the feminine at the cost of the masculine.  Molina understands that his own conception of gender is something that can change, and that being born one way is not something that remains fixed.  Molina's occupation as a window dresser is also reflective of how gender identity is constantly "under construction" for both ourselves and others.  Even Valentin, who comes across as the stereotypical political male to start the drama, moves into a different identity in gender as he becomes Molina's lover.  This helps to bring out the idea that gender identity is fluid and is not fixed.  The way in which one sees themselves in terms of gender is not something decided by the external world, but rather is something that one can envision as part of one's own subjectivity.  This recognition becomes critical, in that one's own view of oneself in terms of gender is something embraced or something that is acknowledged by the individual.

What is the portrayal of gender roles in Kiss of the Spider Woman?

Your question can refer both to the writer Manuel Puig's authorial attitude toward gender roles in general and the one that is presented by him through this particular novel—they do not necessarily have to be one and the same. When it comes to Puig, he is known for deliberately subverting traditional gender roles, especially those within deeply traditional cultures (for example, in his native Argentina). Through his novels (including Kiss of the Spider Woman) Puig often playfully and sometimes cynically questions the traditional masculine model of behavior—the one which dictates that the man should be unemotional, principled, and tough—by infusing his male characters with what used to be considered typically feminine traits. His female characters, on the other hand, become “spider-women”: predators in search of (male) prey.

In Kiss of the Spider Woman, Puig presents us at the beginning of the novel (through dialogue) with a typically macho male character, Valentin, who is a revolutionary, and Molina, a female impersonator who may be a transgender woman. However, over the course of the novel, they subtly “change roles”—Molina becomes more proactive and domineering, while Valentin embraces his own gentler side. In this way Puig shows us that gender is a construct which is molded through our perceptions and expectations, and in this novel he manipulates the characters so that we find our own ideas about gender roles a little bit destabilized.