Let $n \in \mathbb{N}$, $p$ a prime number, and $G$ a finite group of order coprime to $p$. Let $R = \mathbb{Z} /p^n \mathbb{Z}$ be the ring of integers mod $p^n$. Must $R[G]$ be semisimple?

As noted in the comments, since $R$ itself is not semisimple this can not be true.

What if $R$ is semisimple (and has characteristic $p$)? Is there some generalization of Maschke's theorem valid here?