## The Stringy K-theory and Cohomology of Orbifolds and the Chern
Character

Takashi Kimura, Boston University

Abstract:

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.