  We study the quantum phases of a three-color Hubbard model that arises in the
dynamics of the p-band orbitals of spinless fermions in an optical lattice.
Strong, color-dependent interactions are induced by an optical Feshbach
resonance. Starting from the microscopic scattering properties of ultracold
atoms, we derive the orbital exchange constants at 1/3 filling on the cubic
optical lattice. Using this, we compute the phase diagram in a Gutzwiller
ansatz. We find novel phases with 'axial orbital order' in which pz and px +
ipy (or px - ipy) orbitals alternate.
