Title: Frobenius induction for algebras Authors: T. Coconet and A. Marcus and C.C. Todea; Abstract: Let $B\to A$ be a homomorphism of Hopf algebras and let $C$ be an algebra. We consider the induction from $B$ to $A$ of $C$ in two cases: when $C$ is a $B$-interior algebra and when $C$ is a $B$-module algebra. Our main results establish the connection between the two inductions. The inspiration comes from finite group representation theory, and some constructions work in even more general contexts. Satus: Accepted/2016/ Comm. Alg.