K-theoretic and categorical properties of toric Deligne-Mumford stacks - Coates,T; Iritani,H; Jiang,Y; Segal,EP (Pure and Applied and Mathematics Quarterly, 2015)
We prove the following results for toric Deligne–Mumford stacks, under minimal compactness hypotheses: the Localization Theorem in equivariant KK-theory; the equivariant Hirzebruch–Riemann–Roch theorem; the Fourier–Mukai transformation associated to a crepant toric wall-crossing gives an equivariant derived equivalence.