\title{Blocks inequivalent to their Frobenius twists}
\author{David  Benson, Radha Kessar}

\address {Department of Mathematics, University of Aberdeen,
King's College, Aberdeen AB24 3UE, Scotland }

\begin{abstract}
Let $k$ be an algebraically closed field of characteristic $p$.
We give a general method for producing 
examples of blocks $B$ of finite group algebras that are 
not Morita equivalent as $k$-algebras to the Frobenius twist $B^{(p)}$. 
Our method produces non-nilpotent blocks having one simple module and 
elementary abelian defect group. 
These also provide the first known examples of  blocks  where
there is a perfect isotypy at the level of ordinary characters
with all the signs positive, but
no derived equivalence between the blocks. 

We do not know of any examples
of blocks $B$ that are not Morita equivalent to the second
Frobenius twist $B^{(p^2)}$.
\end{abstract}