  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 are
generic. We formulate a conjecture on the simple perversity of these complexes,
and we prove it in the level two case (thus generalised a result of Lusztig
from the function field case). We then discuss the induction and restriction
functors, as well as the Frobenius reciprocity, based on the perversity.
