Abstract

We develop methods for computing graded Ktheory of C*algebras
as defined in terms of Kasparov theory. We establish graded versions
of Pimsner’s sixterm exact sequences for graded Hilbert bimodules whose
left action is injective and by compacts, and a graded Pimsner–Voiculescu sequence.
We introduce the notion of a twisted Pgraph C*algebra and establish
connections with graded C*algebras. Specifically, we show how a functor
from a Pgraph into the group of order two determines a grading of the associated
C*algebra. We apply our graded version of Pimsner’s exact sequence to
compute the graded Ktheory of a graph C*algebra carrying such a grading.