Fixed point actions for free and interacting staggered lattice fermion
s are constructed by iterating renormalization group transformations.
At large N the fixed point action for the Gross-Neveu model is a perfe
ct action in the sense of Hasenfratz and Niedermayer, i,e, cut-off eff
ects are completely eliminated. Tn particular, the fermionic 1-particl
e energy spectrum of the lattice theory is identical with the one of t
he continuum even for arbitrarily small correlation lengths. The cut-o
ff effects of the chiral condensate are eliminated using a perfect ope
rator.