Kymlicka is the theorist who made multiculturalism an argument liberals had to answer on their own terms rather than a communitarian objection to liberalism.
His premise is orthodox liberal: what matters is individual autonomy, the capacity to form and revise a conception of the good. His addition is that autonomy is not exercised in a vacuum. Meaningful choice requires a range of options presented as valuable, and that range is supplied by what he calls a societal culture — a shared language and set of institutions covering the full range of human activity. People are not attached to their culture for its own sake so much as dependent on it for the materials of choice.
From this the political conclusion follows. Members of a majority get their societal culture maintained automatically by the state, which conducts business in their language, keeps their holidays and teaches their history. Minorities do not, and the difference is not neutrality but an unmarked subsidy. Group-differentiated rights — language guarantees, self-government for national minorities, accommodations for immigrant groups — correct that asymmetry, and are therefore a requirement of liberal equality rather than a departure from it.
The distinction he insists on is between external protections, which shield a group from the decisions of the larger society and are legitimate, and internal restrictions, which a group imposes on its own dissenting members and are not. A liberal multiculturalism protects cultures from erosion but never authorizes them to coerce their own.
He also distinguishes national minorities, incorporated involuntarily and with a claim to self-government, from immigrant groups who chose to move and whose claims are to fair terms of integration — a distinction that has drawn as much criticism as the rest of the theory.