  We extend Ravenel-Wilson Hopf ring techniques to $C_2$-equivariant homotopy
theory. Our main application and motivation is a computation of the
$RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacLane spaces. The
result we obtain for $C_2$-equivariant Eilenberg-MacLane spaces associated to
the constant Mackey functor $\underline{\mathbb{F}}_2$ gives a
$C_2$-equivariant analogue of the classical computation due to Serre. We also
investigate a twisted bar spectral sequence computing the homology of these
equivariant Eilenberg-MacLane spaces and suggest the existence of another
twisted bar spectral sequence with $E^2$-page given in terms of a twisted Tor
functor.
