Suppose that $O=\mathbb{F}_q[\pi ]$ is a polynomial ring and $R$ is a commutative unitary $O$-algebra. The category of finite flat group schemes over $R$ with a strict action of $O$ was recently introduced by Faltings and appears as an equal characteristic analogue of the classical category of finite flat group schemes in the equal characteristic case. In this paper we obtain a classification of these modules and apply it to prove analogues of properties that were known earlier for classical group schemes.