Authors:  Apostolos Beligiannis and Henning Krause.
Addresses: Department of Mathematics, 
             University of the Aegean
             82300 Karlovassi, Samos,
             Greece,
       and 
             Fakult\"{a}t f\"{u}r Mathematik, 
             Universit\"{a}t Bielefeld,
             D-33501 Bielefeld, 
             Germany.
             

Article: "Realizing maps between modules over Tate cohomology
             rings"

Status: Submitted for publication. 

Abstract: Let $G$ be a finite group and $k$ be a field.
Given two representations $A$ and $B$ of $G$,
we investigate when all homomorphisms 
$\widehat H^*(G,A)\to\widehat H^*(G,B)$
over the Tate cohomology ring $\widehat H^*(G,k)$ are 
of the form $\widehat H^*(G,\alpha)$ for some morphism
$\alpha\colon A\to B$. We construct an extended Milnor 
sequence which computes the obstruction for homomorphisms
$\widehat H^*(G,A)\to\widehat H^*(G,B)$ to be realizable.