  We study whether applying lattice projectors on a vector-like Ginsparg-Wilson
Dirac operator is the only way to construct left-handed lattice fermions. Using
RG transformations we derive an equation for the generating functional on the
lattice, obtained by blocking from the continuum. We analyze how symmetries of
the continuum theory manifest themselves in this lattice generating functional
and how anomalies emerge. The formalism is applied to left-handed continuum
fermions and we derive two equations that characterize the corresponding
lattice symmetries. To analyze possible solutions, we directly block a
parameterized action for free continuum fermions to obtain the corresponding
lattice action. Subsequently we study parameter values where the continuum
action corresponds to left-handed fermions.
