 Splitting p-modular system

Here $\mathcal{O}$ is a complete discrete valuation ring with fraction field $K$ of characteristic zero and residue field $k$ of characteristic $p$. The system is splitting for the finite group and its subgroups when their simple representations over $K$ and $k$ are absolutely irreducible. It permits ordinary and modular representation theory to be compared by reduction of lattices modulo the maximal ideal.