Stringy product on twisted orbifold K-theory for abelian quotients

In this paper we present a model to calculate the stringy product on twisted orbifold K-theory of Adem-Ruan-Zhang for abelian complex orbifolds. In the first part we consider the non-twisted case on an orbifold presented as the quotient of a manifold acted by a compact abelian Lie group. We give an explicit description of the obstruction bundle, we explain the relation with the product defined by Jarvis-Kaufmann-Kimura and, via a Chern character map, with the Chen-Ruan cohomology, and we explicitely calculate the stringy product for a weighted projective orbifold. In the second part we consider orbifolds presented as the quotient of a manifold acted by a finite abelian group and twistings coming from the group cohomology. We show a decomposition formula for twisted orbifold K-theory that is suited to calculate the stringy product and we use this formula to calculate two examples when the group is $(\integer/2)^3$.

💡 Research Summary

The paper develops an explicit computational framework for the stringy product on twisted orbifold K‑theory in the setting of abelian quotients. It is divided into two main parts: the untwisted case for orbifolds presented as quotients of manifolds by compact abelian Lie groups, and the twisted case for quotients by finite abelian groups with twistings coming from group cohomology.

In the first part the authors consider an orbifold (