  On a smooth closed oriented $4$-manifold $M$ with a smooth action of a finite
group $G$ on a Spin$^c$ structure, $G$-monopole invariant is defined by
"counting" $G$-invariant solutions of Seiberg-Witten equations for any
$G$-invariant Riemannian metric on $M$.
  We compute $G$-monopole invariants on some $G$-manifolds. For example, the
connected sum of $k$ copies of a 4-manifold with nontrivial mod 2
Seiberg-Witten invariant has nonzero $\Bbb Z_k$-monopole invariant mod 2, where
the $\Bbb Z_k$-action is given by cyclic permutations of $k$ summands.
