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We construct a Baum–Connes assembly map localised at the unit element of a discrete group 
$\Gamma$. This morphism, called 
$\mu _\tau$, is defined in 
$KK$-theory with coefficients in 
$\mathbb {R}$ by means of the action of the idempotent 
$[\tau ]\in KK_{\mathbin {{\mathbb {R}}}}^\Gamma (\mathbb {C},\mathbb {C})$ canonically associated to the group trace of 
$\Gamma$. We show that the corresponding 
$\tau$-Baum–Connes conjecture is weaker than the classical version, but still implies the strong Novikov conjecture. The right-hand side of 
$\mu _\tau$ is functorial with respect to the group 
$\Gamma$.
Given a group G and a ring R, Loday [Lod, 1976] described an assembly map αG : hn(BG;L(R)) → Kn(RG) where L(R) is a spectrum with nth space K0(SnR) × BGL(SnR)+ for n ≥ 0 and Kn(RG) = πn(BGL(RG)+ × K0(RG)). Hambleton and Pederson, [HP, 2004], indicate a proof that this map is isomorphic to the map on homotopy groups from the assembly map 
. We will complete the proof of this.
