  We propose a lattice action for two dimensional super Yang-Mills theory with
a twisted N=2 supersymmetry. The extended supersymmetry is fully and exactly
realized on the lattice. The method employed is quite general and its extension
to the N=4 supersymmetry in four dimensions is briefly presented. The lattice
has a new type of ``fermionic'' links, where odd Grassmann variables,
supercharges and fermionic connections sit. The Leibniz rule is preserved on
the lattice, although in a modified ``shifted'' form that takes into account
the link nature of both derivatives and supercharges. Superfields are
semi-local objects and superfield expansion is naturally embedded in the
lattice structure. The Dirac-K\"ahler twist generates the extended twisted
supersymmetry, turning the multiplicity of species doublers into the
multiplicity due to the extended supersymmetry. In this way the balance between
bosonic and fermionic degrees of freedom is preserved.
