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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 
$\Gamma$.
