Lattice Regularization and Symmetries
  Finding the relation between the symmetry transformations in the continuum and on the lattice might be a nontrivial task as illustrated by the history of chiral symmetry. Lattice actions induced by a renormalization group procedure inherit all symmetries of the continuum theory. We give a general procedure which gives the corresponding symmetry transformations on the lattice. 
Peter Hasenfratz, Ferenc Niedermayer, Reto von Allmen