D.J.Benson and J.Greenlees.
The action of the Steenrod algebra on Tate cohomology.
J. Pure & Applied Algebra 85 (1993), 21-26.
MR 94b:55023
\begin{abstract}
Let $G$ be a finite group and $k$ a field of characteristic $p$ dividing 
$|G|$. In this paper, we examine the action of the Steenrod operations on the 
Tate cohomology $\hat{H}^*(G,k)$. In particular, we prove that all Steenrod 
operations from negative to positive degree Tate cohomology vanish if and only 
if all products in negative degree Tate cohomology vanish.
\end{abstract}