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We show that for any finite $p$-group $P$ of rank at least 2 and anyalgebraically 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 ineach even degree. In particular, this provides examples of symmetric algebras$A$ for which $Z^0(\modbar(A))$ is not finite-dimensional, answering a questionraised in [10]

On the graded center of the stable category of a finite $p$-group