Kac Algebras Arising From Composition Of Subfactors

Deals with a map $\alpha$ from a finite group $G$ into the automorphism group $Aut({\mathcal L})$ of a factor ${\mathcal L}$ satisfying: $G=N \rtimes H$ is a semi-direct product, and the induced map $g \in G \to (\alpha_g) \in Out({\mathcal L})=Aut({\mathcal L})/Int({\mathcal L})$ is an injective homomorphism.