The Baum-Connes conjecture localised at the unit element of a discrete group

We construct a Baum-Connes assembly map localised at the unit element of a discrete group. This morphism, called, is defined in -theory with coefficients in by means of the action of the idempotent canonically associated to the group trace of. We show that the corresponding -Baum-Connes conjecture is weaker than the classical version, but still implies the strong Novikov conjecture. The right-hand side of is functorial with respect to the group.