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Operations in equivariant ℤ/p-cohomology

If G is a compact Lie group and M a Mackey functor, then Lewis, May and McClure [4] define an ordinary cohomology theory H*G(−; M) on G-spaces, graded by representations. In this article, we compute the ℤ/p-rank of the algebra of integer-degree stable operations [Ascr ]M, in the case where G=ℤ/p and M is constant at ℤ/p. We also examine the relationship between [Ascr ]M and the ordinary mod-p Steenrod algebra [Ascr ]p. The main result implies that while [Ascr ]M is quite large, its image in [Ascr ]p consists of only the identity and the Bockstein. This is in sharp contrast to the case with M constant at ℤ/p for q≠p; there [Ascr ]M≅[Ascr ]q.