Cohomology of groups and splendid equivalences of derived categories
by Alexander Zimmermann;
to appear in Mathematical Proceedings of the Cambridge Philosophical Society
(slightly modfied version to the earlier preprint)


The stabilizer of the trivial module in the group of 
auto-equivalences of the derived category of 
the principal block of a group ring $kG$ over a field $k$ of
characteristic $p$ acts on the cohomology ring of the group 
$G$. It is shown that taking only splendid equivalences 
as introduced by J. Rickard then, this action is compatible 
with respect to restriction and transfer to centralizers
of $p$-subgroups.