On the KK-theory of twisted higher-rank-graph C∗C∗-algebras

We investigate the KK-theory of twisted higher-rank-graph algebras by adapting parts of Elliott’s computation of the KK-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group determines a continuous bundle of twisted higher-rank graph algebras over the dual group. We use this to show that for a circle-valued 2-cocycle on a higher-rank graph obtained by exponentiating a real-valued cocycle, the KK-theory of the twisted higher-rank graph algebra coincides with that of the untwisted one.