On fusion algebras associated to finite group actions

In our previous paper (see Kosaki and Yamagami), four kinds of bimodules naturally attached to crossed products P ⋊ G ⊇ P ⋊ H determined by a group-subgroup pair G ⊇ H were identified with certain vector bundles equipped with group actions. In the present paper we will describe the structure of the fusion algebra of vector bundles and clarify a relationship to fusion algebras appearing in other contexts. Some applications to automorphism analysis for subfactors will be also given.