** A Maschke Type Theorem for Weak Relative Hopf ***π*-Modules

* Shuangjian Guo *

*π*-Modules

**Abstract**

Let *H* be a weak Hopf *π*-coalgebra and let *A* be a weak right *π*-*H*-comodule algebra with a total integral *ϕ*. This paper is mainly devoted to a Maschke type theorem for (*H*,*A*)-weak relative Hopf *π*-modules. As an application, we obtain a characterization for an (*H*,*A*)-weak Hopf *π*-module to be projective as an *A*-module.