Twisted orbifold K-theory for global quotient

Let [X/G] be the global quotient of a complex manifold X by a finite group G, with a twisting α∈Z2(G,S1). Adem and Ruan defined the twisted orbifold K-theory Korbα(X/G). In this paper, we construct a decomposition for Korbα(X/G) and define a product on Korbα(X/G) using the method of stringy product. Then we construct a twisted Chern characterChorbα:αKorb(X/G)⊗C⟶Horb⁎(X/G;Lα). Here Horb⁎(X/G;Lα) is the twisted orbifold cohomology of [X/G]. Furthermore we show that this twisted Chern character is a ring isomorphism.