We propose a new formulation which realizes exact twisted supersymmetry for
all the supercharges on a lattice by twisted superspace formalism. We show
explicit examples of N=2 twisted supersymmetry invariant BF and Wess-Zumino
models in two dimensions. We introduce mild lattice noncommutativity to
preserve Leibniz rule on the lattice. The formulation is based on the twisted
superspace formalism for N=D=2 supersymmetry which was proposed recently. From
the consistency condition of the noncommutativity of superspace, we find an
unexpected three-dimensional lattice structure which may reduce into two
dimensional lattice where the superspace describes semilocally scattered
fermions and bosons within a double size square lattice.Comment: 49 pages, 17 figures; v2: Fig.2 is replace
