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.