  Existence results for a class of Choquard equations with potentials are
established. The potential has a limit at infinity and it is taken invariant
under the action of a closed subgroup of linear isometries of $\mathbb{R}^N$.
As a consequence, the positive solution found will be invariant under the same
action. Power nonlinearities with exponent greater or equal than two or less
than two will be handled. Our results include the physical case.
