\author{Dave Benson} \author{Radha Kessar} \author{Markus Linckelmann} \title{On the BV structure of the Hochschild cohomology of finite group algebras} \begin{document} \begin{abstract} We give a simple algebraic recipe for calculating the components of the BV operator $\Delta$ on the Hochschild cohomology of a finite group algebra with respect to the centraliser decomposition. We use this to investigate the properties of $\Delta$ and to make some computations for some particular finite groups. \end{abstract}