  Let C be a complex smooth projective algebraic curve endowed with an action
of a finite group G such that the quotient curve has genus at least 3. We prove
that if the G-curve C is very general for these properties, then the natural
map from the group algebra QG to the algebra of Q-endomorphisms of its Jacobian
is an isomorphism. We use this to obtain (topological) properties regarding
certain virtual linear representations of a mapping class group. For example,
we show that the connected component of the Zariski closure of such a
representation acts Q-irreducibly in a G-isogeny space of H^1(C; Q)and with
image often a Q-almost simple group.
