  Let G be a finite group acting on a smooth projective curve X. This induces
an action of G on the Jacobian JX of X and thus a decomposition of JX up to
isogeny. The most prominent example of such a situation is the group G of two
elements. Let X --> Y denote the corresponding quotient map. Then JX is
isogenous to the product of JY with the Prym variety of X/Y. In this paper some
general results on group actions on abelian varieties are given and applied to
deduce a decomposition of the jacobian JX for arbitrary group actions. Several
examples are given.
