The study of smooth representations of p-adic reductive groups over fields of characteristic p is at the heart of the mod p Langlands program. If G denotes such a group and I denotes a pro-p Iwahori subgroup, a natural tool that one might use to study these representations is to pass to the so-called pro-p Iwahori-Hecke algebra H. There is a natural adjunction between the categories of smooth G-representations and H-modules, which is known to give rise to various useful equivalences of categories when working in characteristic different than p. However, in characteristic p the behaviour of this adjunction is not sufficiently understood beyond GL_2(Q_p) and a few related cases. In this talk, I will present a new approach to study this adjunction using the language of model categories. The Hecke algebra H is known by work of Ollivier-Schneider to be Gorenstein, and from work of Hovey it follows that its category of modules has a so-called Gorenstein projective model structure. We use this to define a model structure on smooth G-representations. Our adjunction then naturally induces an adjunction between homotopy categories whose behaviour can be better understood. Along the way, we generalise a result of Cabanes on representations of finite reductive groups. This is joint work with Jan Kohlhaase.