Operations in equivariant Z/p-cohomology

If G is a compact Lie group and M a Mackey functor, then Lewis, May and McC lure [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 algebr a of integer-degree stable operations A(M), in the case where G = Z/p and M is constant at Z/p. We also examine the relationship between A(M), and the ordinary mod-p Steenrod algebra A(p). The main result implies that while A(M) is quite large, its image in A(p) c onsists of only the identity and the Bockstein. This is in sharp contrast t o the case with M constant at Z/p for q not equal p; there A(M) congruent t o A(q).