Strong Novikov conjecture for the analytic assembly map

Let $\pi$ be a discrete group, let $B\pi$ be its classifying space, and let $C^*(\pi)$ denote the relevant group $C^*$-algebra. The analytic assembly map is

$$\alpha:KO_*(B\pi)\longrightarrow KO_*(C^*(\pi)).$$

Strong Novikov conjecture. The analytic assembly map $\alpha$ is a monomorphism. This is the injectivity statement connecting $KO$-homology of the classifying space to the $K$-theory of the group $C^*$-algebra; the source uses it as an assumption in its theorem and does not state a resolution.