The theorem of Szemeredi on existence of arbitrarily long arithmetic progressions in sets of integers of positive density is known to be equivalent to a "multiple recurrence" theorem for ergodic measure preserving dynamical systems. An analogous theorem for non-amenable groups can be demonstrated by introducing the notion of a "stationary group action" where measure need not be preserved. Based on this one can formulate conditions on subsets of an arbitrary group that guarantee existence of arbitrarily long geometric progressions. These conditions can be made explicit for a finitely generated free group.