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The Ginsparg-Wilson relation is extended to interacting field theories withgeneral linear symmetries. Our relation encodes the remnant of the originalsymmetry in terms of the blocked fields and guides the construction ofinvariant lattice actions. We apply this approach in the case of latticesupersymmetry. An additional constraint has to be satisfied because of theappearance of a derivative operator in the symmetry transformations. Thesolution of this constraint leads to non-local SLAC-type derivatives. Weinvestigate the corresponding kinetic operators on the lattice within an exactsolution of supersymmetric quantum mechanics. These solutions - analogues ofthe overlap operator for supersymmetry - can be made local through a specificchoice of the blocking kernel. We show that the corresponding relation allowsfor local lattice symmetry operators as well as local lattice actions. We arguethat for interacting theories the lattice action is polynomial in the fieldsonly under special circumstances, which is exemplified within an exactsolution.

Generalising the Ginsparg-Wilson relation: Lattice Supersymmetry from Blocking Transformations