  We study the center of the pro-p Iwahori-Hecke ring H of a connected split
p-adic reductive group G. For k an algebraically closed field with
characteristic p, we prove that the center of the k-algebra H_k:= H\otimes_Z k
contains an affine semigroup algebra which is naturally isomorphic to the Hecke
algebra attached to any irreducible smooth k-representation of a given
hyperspecial maximal compact subgroup of G. This isomorphism is obtained using
the inverse Satake isomorphism constructed in arXiv:1207.5557. We apply this to
classify the simple supersingular H_k-modules, study the supersingular block in
the category of finite length H_k-modules, and relate the latter to
supersingular representations of G.
