We describe Universal Coefficient Theorems for the equivariant Kasparov theory for C*-algebras with an action of the group of integers or over a unique path space, using KK-valued invariants. We compare the resulting classification up to equivariant KK-equivalence with the recent classification theorem involving a K-theoretic invariant together with an obstruction class in a certain Ext^2-group and with the classification by filtrated K-theory. This is based on a general theorem that computes these obstruction classes.
Categories: math.KT