  We consider dipolar fermions in a two-dimensional square lattice and a
harmonic trapping potential. The anisotropy of the dipolar interaction combined
with the lattice leads to transitions between phases with density order of
different symmetries. We show that the attractive part of the dipolar
interaction results in a superfluid phase which is suppressed by density order.
The trapping potential is demonstrated to make the different phases co-exist,
forming ring and island structures. The phases with density and superfluid
order can overlap forming regions with supersolid order.
