Abstract
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 = $G={\mathbb{Z}}$ 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.
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