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A decomposition of equivariant K-theory in twisted equivariant K-theories (1604.01656v2)
Published 6 Apr 2016 in math.KT and math.AT
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.