Delocalized Chern character for stringy orbifold K-theory

Hu, Jianxun; Wang, Bai-Ling

doi:10.1090/S0002-9947-2013-05834-5

Delocalized Chern character for stringy orbifold K-theory

Authors: Jianxun Hu and Bai-Ling Wang
Journal: Trans. Amer. Math. Soc. 365 (2013), 6309-6341
MSC (2010): Primary 57R19, 19L10, 22A22; Secondary 55N15, 53D45
DOI: https://doi.org/10.1090/S0002-9947-2013-05834-5
Published electronically: June 4, 2013
MathSciNet review: 3105753
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Abstract: In this paper, we define a stringy product on $K^*_{orb}(\mathfrak{X}) \otimes \mathbb{C}$ , the orbifold K-theory of any almost complex presentable orbifold $\mathfrak{X}$ . We establish that under this stringy product, the delocalized Chern character

$\displaystyle ch_{deloc} : K^*_{orb}(\mathfrak{X}) \otimes \mathbb{C} \longrightarrow H^*_{CR}(\mathfrak{X}),$

after a canonical modification, is a ring isomorphism. Here $H^*_{CR}(\mathfrak{X})$ is the Chen-Ruan cohomology of $\mathfrak{X}$ . 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

of a finite group

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).

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