  We show that for any finite $p$-group $P$ of rank at least 2 and any
algebraically closed field $k$ of characteristic $p$ the graded center
$Z^*(\modbar(kP))$ of the stable module category of finite-dimensional
$kP$-modules has infinite dimension in each odd degree, and if $p=2$ also in
each even degree. In particular, this provides examples of symmetric algebras
$A$ for which $Z^0(\modbar(A))$ is not finite-dimensional, answering a question
raised in [10]
