Fusion rings arising from normal Hopf subalgebras

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 $G={\mathbb{Z}}_p$ this ring determines a fusion ring and we give a complete description for it. The case $G={\mathbb{Z}}_{p^n}$ and some other applications are presented.