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Description:
The notion of order in triangulated categories, as introduced by Schwede, is investigated in the case of the stable category of kG -modules, where k is a field of characteristic p and G is a finite group. For Tate cohomology classes ζ of even degree, we obtain bounds on the ζ -order which are similar to corresponding results on the p -order in the stable homotopy category. On our way we introduce a power operation P 1 on Tate cohomology which serves as an obstruction for the ζ -order to be larger than its minimal possible value. Furthermore, it enables us to compute certain higher Massey products explicitly.