  A gas of strongly interacting spinless p-orbital fermionic atoms in 2D
optical lattices is proposed and studied. Several interesting new features are
found. In the Mott limit on a square lattice, the gas is found to be described
effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2
XXZ model. For a triangular, honeycomb, or Kagome lattice, the orbital exchange
is geometrically frustrated and described by a new quantum 120 degree model. We
determine the orbital ordering on the Kagome lattice, and show how orbital wave
fluctuations select ground states via the order by disorder mechanism for the
honeycomb lattice. We discuss experimental signatures of various orbital
ordering.
