A decomposition of equivariant K-theory in twisted equivariant K-theories

Abstract

For G a finite group and X a G-space on which a normal subgroup A acts trivially, we show that the G-equivariant K-theory of X decomposes as a direct sum of twisted equivariant K-theories of X parametrized by the orbits of the conjugation action of G on the irreducible representations of A. The twists are group 2-cocycles which encode the obstruction of lifting an irreducible representation of A to the subgroup of G which fixes the isomorphism class of the irreducible representation.

Shorter version version. 20 pages. Accepted for publication in IJM

References in corpus (1)

• Twisted Orbifold K-Theory

Cited by in corpus (2)

• Equivariant complex bundles, fixed points and equivariant unitary bordism
• The Duistermaat-Heckman formula with application to circle actions and Poincaré $q$-polynomials in twisted equivariant K-theory