  We study the extended Hubbard model away from half-filling on a
two-dimensional square lattice using cluster dynamical mean field theory on
clusters of size $8$. We show that the model exhibits metallic, compressible
charge ordered, and insulating charge ordered phases. We determine the location
of the charge ordering phase transition line at finite temperature and the
properties of the phases as a function of doping, temperature, local
interaction, and nearest neighbor interaction. An analysis of the energetics of
the charge order transition shows that the charge ordering transition mainly
results in a rearrangement of local and non-local potential energy. We show the
doping evolution of the spectral function from the isotropic metal via a charge
ordered metal to a charge ordered insulator with a big gap, and study finite
size effects of the approximation.
