  For any normal commutative Hopf subalgebra $K=k^G$ of a semisimple Hopf
algebra we describe the ring inside $kG$ obtained by the restriction of
$H$-modules. If $G=\Z_p$ this ring determines a fusion ring and we give a
complete description for it. The case $G=\Z_{p^n}$ and some other applications
are presented.
