Delocalized chern character for stringy orbifold K-theory

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 delocalized Chern character ch_deloc: K*_orb(X) ⊗ ℂ -→ H*_{C R}(X), after a canonical modification, is a ring isomorphism. Here H*_{C R}(X) is the Chen-Ruan cohomology of X. The proof relies on an intrinsic description of the obstruction 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 product is different from the Pontryagin product (the latter is also called the fusion product in string theory).