My question is the following:
Let M be a simply connected Riemannian manifold whose sectional curvatures are all nonpositive and let G be a group. Suppose that G acts in M properly discontinuous and cocompactly by isometries. Is G a CAT(0) group?
My question is the following: Let M be a simply connected Riemannian manifold whose sectional curvatures are all nonpositive and let G be a group. Suppose that G acts in M properly discontinuous and cocompactly by isometries. Is G a CAT(0) group? 


The answer is yes, since $M$ is a $CAT(0)$ space, and the group is quasiisometric to it. See (for example) Jim Cannon's article in Bedford Keane Series: The theory of negatively curved spaces and groups J Cannon  t. Bedford, M. Keane, and C. Series. Oxford University …, 1991 

