Let F be a nite extension of Qp. We associate, to certain smooth p-modular representations Pi of GL2(F), a module S(Pi) on the mod p Iwasawa of the standard Iwahori subgroup I of GL2(F). When F is unramied, we obtain a module on a suitable formally smooth Fq-algebra, endowed with an action of OxF (the units in the ring of integers of F) and an OxF equivariant, Frobenius semilinear endomorphism which turns out to be étale. We study the torsion properties of such module, as well as its Iwahori-radical ltration.