Coarse and equivariant co-assembly maps
  We study an equivariant co-assembly map that is dual to the usual Baum-Connes assembly map and closely related to coarse geometry, equivariant Kasparov theory, and the existence of dual Dirac morphisms. As applications, we prove the existence of dual Dirac morphisms for groups with suitable compactifications, that is, satisfying the Carlsson-Pedersen condition, and we study a K-theoretic counterpart to the proper Lipschitz cohomology of Connes, Gromov and Moscovici. 
Heath Emerson and Ralf Meyer