  Let $G$ denote a finite group and $\pi: Z \to Y$ a Galois covering of smooth
projective curves with Galois group $G$. For every subgroup $H$ of $G$ there is
a canonical action of the corresponding Hecke algebra $\mathbb{Q}[H \backslash
G/H]$ on the Jacobian of the curve $X = Z/H$. To each rational irreducible
representation $\mathcal{W}$ of $G$ we associate an idempotent in the Hecke
algebra, which induces a correspondence of the curve $X$ and thus an abelian
subvariety $P$ of the Jacobian $JX$. We give sufficient conditions on
$\mathcal{W}$, $H$, and the action of $G$ on $Z$, which imply $P$ to be a
Prym-Tyurin variety. We obtain many new families of Prym-Tyurin varieties of
arbitrary exponent in this way.
