Delocalized Chern character for stringy orbifold K-theory

Abstract

In this paper, we define a stringy product on $K^*_{orb}(\XX) \otimes \C $, the orbifold K-theory of any almost complex presentable orbifold $\XX$. We establish that under this stringy product, the de-locaized Chern character ch_{deloc} : K^*_{orb}(\XX) \otimes \C \longrightarrow H^*_{CR}(\XX), after a canonical modification, is a ring isomorphism. Here $ H^*_{CR}(\XX)$ is the Chen-Ruan cohomology of $\XX$. The proof relies on an intrinsic description of the obstruction bundles in the construction of Chen-Ruan product. As an application, we investigate this stringy product on the equivariant K-theory $K_G^{\ast }(G)$ of a finite group $G$ with the conjugation action. It turns out that the stringy product is different from the Pontryajin product (the latter is also called the fusion product in string theory).

34 pages. Final version to appear in Trans. of AMS. Improve the expositions and Change of the title thanks the referees

References in corpus (2)

• Logarithmic trace and orbifold products
• The Full Orbifold $K$-theory of Abelian Symplectic Quotients