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In this paper, we introduce the notion of an EZ-structure on a group, an equivariant version of the Z-structures introduced by Bestvina . Examples of groups having an EZ-structure 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 properdoi:10.4171/cmh/7 fatcat:6zgpsexl7rgazmkuhzw5fe44wi