The goal of this paper is to show explicitly the construction of a Cartan-Eilenberg system for the twisted equivariant K-theory groups of a finite G-CW complex, with G a finite group. Such a system defines a spectralsequence, whose second page is given by the Cˇech cohomology of a presheaf associated to projective representations of isotropy groups.

The goal of this paper is to show explicitly the construction of a Cartan-Eilenberg system for the twisted equivariant K-theory groups of a finite G-CW complex, with G a finite group. Such a system defines a spectralsequence, whose second page is given by the Cˇech cohomology of a presheaf associated to projective representations of isotropy groups.