The Full Orbifold K-theory of Abelian Symplectic Quotients

In their 2007 paper, Jarvis, Kaufmann, and Kimura defined the full orbifold K-theory of an orbifold X, analogous to the Chen-Ruan orbifold cohomology of X in that it uses the obstruction bundle as a quantum correction to the multiplicative structure. We give an explicit algorithm for the computation of this orbifold invariant in the case when X arises as an abelian symplectic quotient. Our methods are integral K-theoretic analogues of those used in the orbifold cohomology case by Goldin, Holm, and Knutson in 2005. We rely on the K-theoretic Kirwan surjectivity methods developed by Harada and Landweber. As a worked example, we present the full computation of the full orbifoldK-theory of weighted projective spaces. Our computations hold over the integers, and in the particular case of weighted projective spaces, we show that the associated invariant is torsion-free.