  The exact renormalization group approach (ERG) is developed for the case of
pure fermionic theories by deriving a Grassmann version of the ERG equation and
applying it to the study of fixed point solutions and critical exponents of the
two-dimensional chiral Gross-Neveu model. An approximation based on the
derivative expansion and a further truncation in the number of fields is used.
Two solutions are obtained analytically in the limit $N\to \infty $, with N
being the number of fermionic species. For finite N some fixed point solutions,
with their anomalous dimensions and critical exponents, are computed
numerically. The issue of separation of physical results from the numerous
spurious ones is discussed. We argue that one of the solutions we find can be
identified with that of Dashen and Frishman, whereas the others seem to be new
ones.
