Smooth representations and Hecke modules in characteristicp

Let G be a p-adic Lie group and I ⊆ G be a compact open subgroup which is a torsionfree prop-group.Working over a coefficient field k of characteristic p we introduce a differential graded Hecke algebra for the pair (G, I) and show that the derived category of smooth representations of G in k-vector spaces is naturally equivalent to the derived category of differential graded modules over this Hecke DGA.