Hecke algebra with respect to the pro-p-radical of a maximal compact open subgroup for GL(n,F) and its inner forms

Let G be a direct product of inner forms of general linear groups over non-archimedean locally compact fields of residue characteristic p and let K1 be the pro-p-radical of a maximal compact open subgroup of G. In this paper we describe the (intertwining) Hecke algebra H(G,K1), that is the convolution Z-algebra of functions from G to Z that are bi-invariant for K1 and whose supports are a finite union of K1-double cosets. We produce a presentation by generators and relations of this algebra. Finally we prove that the level-0 subcategory of the category of smooth representations of G over a unitary commutative ring R such that p∈R× is equivalent to the category of modules over H(G,K1)⊗ZR.