Strong Novikov conjecture

Prove that for every discrete group G, the composite $\mu_G\circ\iota_*:K_i(BG)\to K_i(C_r^*(G))$ is rationally injective for i=0,1.

Background

For discrete groups, the strong Novikov conjecture asserts rational injectivity of the assembly map after passing from the K-homology of BG to equivariant K-homology of the classifying space for proper actions. The paper later explains that the existence of a gamma-element implies this conjecture.

References

The following statement is known as the {\bf strong Novikov conjecture} for $G$:

\begin{Conj}\label{SNC} The map $\mu_G\circ\iota_:K_i(BG) K_i(C^_r(G))\;(i=0,1)$ is rationally injective. \end{Conj}

— The Baum-Connes conjecture: a concise course  (2610.01802 - Valette, 1 Oct 2026) in Section 7.3.1, “The strong Novikov conjecture”