The Stringy K-theory and Cohomology of Orbifolds and the Chern Character
Takashi Kimura, Boston University

Associated to a smooth, projective variety with a finite group action is a stringy cohomology ring due to Fantechi-Goettsche whose coinvariants yield the so-called Chen-Ruan orbifold cohomology of the quotient orbifold. These rings were introduced in terms of the Gromov-Witten theory of orbifolds. We present an elementary new definition stringy cohomology which removes all references to complex curves and their moduli. We then introduce stringy K-theory, a K-theoretic version this ring. Finally, we introduce a ring isomorphism between stringy K-theory and the stringy cohomology, called the stringy Chern character, which is a deformation of the ordinary Chern character. As a consequence, the twisted orbifold K-theory of the symmetric product of a projective surface with trivial first Chern class is isomorphic to the ordinary K-theory of its resolution, the Hilbert scheme of points on the surface.