On Gromov's positive scalar curvature conjecture for virtual duality groups

We prove the inequality $$ \dim_{mc}\Wi M\le n-2$$ for the macroscopic dimension of the universal covers $\Wi M$ of almost spin $n$-manifolds $M$ with positive scalar curvature whose fundamental group $\pi_1(M)$ is a virtual duality group that satisfies the coarse Baum-Connes conjecture.