Generic character sheaves on reductive groups over a finite ring

In this paper we propose a construction of generic character sheaves on reductive groups over finite local rings at even levels, whose characteristic functions are higher Deligne–Lusztig characters when the parameters generic. We formulate conjecture simple perversity these complexes, and prove it in level two case (thus extend result Lusztig from function field case). then discuss induction restriction functors , as well Frobenius reciprocity, based perversity.