Equivariant KK-theory for inverse limits of G-C*-algebras

Axiomatic Kk-theory for Real C*-algebras

We establish axiomatic characterizations of K-theory and KK-theory for real C*-algebras. In particular, let F be an abelian group-valued functor on separable real C*-algebras. We prove that if F is homotopy invariant, stable, and split exact, then F factors through the category KK. Also, if F is homotopy invariant, stable, half exact, continuous, and satisfies an appropriate dimension axiom, th...

Equivariant KK-theory and noncommutative index theory

The Universal Property of Equivariant Kk-theory

Let G be a locally compact, σ-compact group. We prove that the equivariant KK-theory, KK, is the universal category for functors from G-algebras to abelian groups which are stable, homotopy invariant and split-exact. This is a generalization of Higsons characterisation of (non-equivariant) KK-theory.

On the Kk-theory of Strongly Self-absorbing C∗-algebras

Let D and A be unital and separable C∗-algebras; let D be strongly selfabsorbing. It is known that any two unital ∗-homomorphisms from D to A ⊗ D are approximately unitarily equivalent. We show that, if D is also K1-injective, they are even asymptotically unitarily equivalent. This in particular implies that any unital endomorphism of D is asymptotically inner. Moreover, the space of automorphi...

KK-theory of reduced free product C*-algebras

0 Introduction For unital C-algebras endowed with states there is a natural reduced free product construction which generalizes the C-algebra of the regular representation of a free product group. Whereas the question of computing the K-theory and all the various KK-groups is completly understood in the case of discrete groups (see the work of Pimsner in 13]), little is known so far for more ge...