  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.
