A Galois-theoretic approach to Kanev's correspondence

Let $G$ be a finite group, $\mathrm{\Lambda }$ an absolutely irreducible $\mathbb{Z}[G]$-module and $w$ a weight of $\mathrm{\Lambda }$. To any Galois covering with group $G$ we associate two correspondences, the Schur and the Kanev correspondence. We work out their relation and compute their invariants. Using this, we give some new examples of Prym-Tyurin varieties.