We compute the equivariant KO-homology of the classifying space for proper actions of SL 3 (Z) and GL 3 (Z). We also compute the Bredon homology and equivariant K-homology of the classifying spaces for proper actions of PSL 2 (Z[ 1 p ]) and SL 2 (Z[ 1 p ]) for each prime p. Finally, we prove the unstable Gromov-Lawson-Rosenberg conjecture for PSL 2 (Z[ 1 p ]) when p ≡ 11 (mod 12).