Twisted Supersymmetry, Fermion-Boson Mixing and Removal of UV-IR Mixing

Exact supersymmetry can be maintained on nonanticommutative superspace with a twisted coproduct on the supergroup.We show that the usual exchange statistics for the superfields is not compatible with the twisted action of the superpoincare group and find a statistics which is consistent with the twisted coproduct and imply interesting phenomena such as mixing of fermions and bosons under particle exchange.We also show that with the new statistics, the $S$-matrix becomes completely independent of the deformation parameter.