  We investigate the fermionic SU(N) Hubbard model on the two-dimensional
square lattice for weak to moderate interaction strengths using one-loop
renormalization group and mean-field methods. For the repulsive case U>0 at
half filling and small N the dominant tendency is towards breaking of the SU(N)
symmetry. For N>6 staggered flux order takes over as the dominant instability,
in agreement with the large-N limit. Away from half filling for N=3 the system
rearranges the particle densities such that two flavors remain half filled by
cannibalizing the third flavor. In the attractive case and odd N a full Fermi
surface coexists with a superconductor in the ground state. These results may
be relevant to future experiments with cold fermionic atoms in optical
lattices.
