Think about the multiple ways that "identity" comes into social life. We think we know what someone means when he says he is African-American, Southern, gen-X, and professional. But of course the reality is much more complex, both within the person and across the group. Each identity label brings with it a cluster of values and attitudes that hang together across a population of people. These clusters are cross-cutting: it may be that there are values shared by many Southerners, both white and black, that differentiate them from Northerners and constitute a dimension of social identity; likewise there is a cluster of values and attitudes shared by African-Americans in both South and North; and so on for youth culture and work culture. (This is sometimes referred to as "intersectionality" and the politics of intersectionality.)
One question we can ask is how these various identities co-exist in one person. How does the individual's psychological system incorporate and process features of identity? How does political and social cognition work at the level of the individual? What determines whether one identity is more salient than another in a given context for a given person? How do the various identity configurations interact within the person; how do behavior and preference result from the several identity configurations? Is there a problem of coherence among the identities? Can one be conflicted over the dictates and affects of the several identities he or she possesses? (Is this illustrated by religious conservative gay politicians?)
Another challenging question is how these identity configurations vary across a population of people who can be said to possess the identity. It is clear that identities are not uniform across a population; it is not the case that there is one profile of "American Baptist" that fits all Baptists. So we need to have some way of conceptualizing how a given identity is instantiated in different ways across individuals within a given group.
We also need a theory of the mechanisms of transmission and maintenance that serve to proliferate an identity across generations and through a population. What are the processes through which individuals and groups acquire their identities? There are some obvious mechanisms--personality development within the family, exposure to values and identities in schools and faith institutions, exposure to identity commitments through the media and the internet. But it would be very useful to have more focused and detailed studies of the ways in which identities are transmitted at the level of the developing individual.
Each of these questions -- the individual-level question and the group-level question -- has implications for political choice and behavior. A political movement requires mobilization of a group of people who are willing to act together for an outcome. And mobilization often depends on the ability of the political organization to amplify some elements of identity within a population and damp down other elements. In India, for example, it is possible to track the efforts of Hindu nationalist parties like the BJP aimed at making religious identity more salient than other civic or economic identities. Contrast this strategy with the strategy of parties like the CPM of West Bengal, which bases its political mobilization on an identity of class.
(Atul Kohli's Democracy and Discontent: India's Growing Crisis of Governability is an excellent discussion of some of these features of identity politics in India.)