I. Hambleton and L. R. Taylor, 
Rational Permutation Modules for Finite Groups 

We study the subring of permutation modules $P(G)$ inside the rational
representation ring $R(G)$ using techniques from induction theory. We
give a criterion to decide when a given rational representation is a
virtual permutation representation. The cokernel $R(G)/P(G)$ is calculated 
in many cases, including $G$ nilpotent.