We describe a construction which associates to any function field k and any place ∞ of k a C-dynamical system (Ck,∞, σt) that is analogous to the Bost-Connes system associated to Q and its archimedian place. Our construction relies on Hayes’ explicit class field theory in terms of signnormalized rank one Drinfel’d modules. We show that Ck,∞ has a faithful continuous action of Gal(K/k), where K ...

We prove that the following are equivalent for a locally compact group G: (i) G is amenable; (ii) M(G) is Connes-amenable; (iii) M(G) has a normal, virtual diagonal.

Using the notion of asymptotic homomorphism due to Connes and Higson we construct bivariant homology-cohomology theories for separable C*-algebras, which satisfy general excision axioms and are nonperiodic.