TITLE: Examples of CAT(0)-groups
QUESTION [6 upvotes]: 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?

REPLY [7 votes]: The answer is yes, since $M$ is a $CAT(0)$ space, and the group is quasi-isometric 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