Complex algebraic stacks and morphisms of intersection complexes

We generalize a construction of Barthel-Brasselet-Fieseler-Gabber-Kaup in the setting of complex varieties to the setting of finite type, complex algebraic stacks. Given two such stacks X, Y with affine stabilizers, and a morphism between them, we construct a morphism from the pullback of the intersection complex of Y to the intersection complex of X. As an application, we show that the Borel-Moore fundamental class of a closed substack Z in a Deligne-Mumford stack X lifts to a class in the intersection cohomology of X.