The stacky concentration theorem

We give a sufficient criterion for the Chow or algebraic bordism groups of an algebraic stack, localized at a set of Chern classes of line bundles, to be concentrated in some closed substack. This is a vast generalization of the torus fixed-point localization theorem in equivariant intersection theory, which is the special case of the stack quotient of a scheme X by an action of a torus T. Taking on the one hand an algebraic stack in place of X, we deduce a generalization of torus localization to algebraic stacks. Taking on the other hand any algebraic group G instead of T, we obtain a localization theorem in G-equivariant intersection theory.