K-Theoretic and Categorical Properties of Toric Deligne--Mumford Stacks
  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. 
Tom Coates, Hiroshi Iritani, Yunfeng Jiang, Ed Segal
math.AG