Delocalized Chern character for stringy orbifold K-theory

Abstract

In this paper, we define a stringy product on K � orb(X) C, the orbifold K-theory of any almost complex presentable orbifold X. We establish that under this stringy product, the delocali zed Chern character chdeloc : K �(X) C ! H � CR(X), after a canonical modification, is a ring isomorphism. Here H � CR(X) is the Chen-Ruan cohomology of X. The proof relies on an intrinsic description of the obstruc tion bundles in the construction of the Chen- Ruan product. As an application, we investigate this stringy product on the equivariant K-theory K � G(G) of a finite group G with the conjugation action. It turns out that the stringy pr oduct is different from the Pontryagin product (the latter is also called the fusion pro duct in string theory).