Abstract. In this paper, we introduce the notion of an EZ-structure on a group, an equivariant version of the Z-structures introduced by Bestvina [4]. Examples of groups having an EZstructure include (1) torsion free δ-hyperbolic groups, and (2) torsion free CAT(0)-groups.Our first theorem shows that any group having an EZ-structure has an action by homeomorphisms on some (D n , ), where n is sufficiently large, and is a closed subset of ∂D n = S n−1 . The action has the property that it is proper and cocompact on D n − , and that if K ⊂ D n − is compact, that diam(gK) tends to zero as g → ∞. We call this property ( * ).Our second theorem uses techniques of to show that the Novikov conjecture holds for any torsion-free discrete group satisfying condition ( * ) (giving a new proof that torsion-free δ-hyperbolic and CAT(0) groups satisfy the Novikov conjecture).Our third theorem gives another application of our main result. We show how, in the case of a torsion-free δ-hyperbolic group , we can obtain a lower bound for the homotopy groups π n (P (B )), where P (·) is the stable topological pseudo-isotopy functor.