  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.
