$K$-theoretic and categorical properties of toric Deligne–Mumford stacks

Abstract

We prove the following results for toric Deligne-Mumford stacks, under minimal compactness hypotheses: the Localization Theorem in equivariant K-theory; the equivariant Hirzebruch-Riemann-Roch theorem; the Fourier-Mukai transformation associated to a crepant toric wall-crossing gives an equivariant derived equivalence.