A more general method to classify up to equivariant KK-equivalence

Abstract

Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results for actions of the circle group on C*-algebras, C*-algebras over finite unique path spaces, and graph C*-algebras with finitely many ideals.

24 pages; added some clarification to the proof of Theorem 2.6, added Remark 3.5, removed incorrect Example 5.21, updated references, acknowledgement and email-address