Let G be the group of rational points of a split connected
reductive group over a nonarchimedean local field of residue
characteristic p.LetI be a pro-p Iwahori subgroup of G and let R be
a commutative quasi-Frobenius ring. If H = R[I\G/I] denotes the
pro-p Iwahori- Hecke algebra of G over R we clarify the relation
between the category of H-modules and the category of G-equivariant
coefficient systems on the semisimple Bruhat-Tits building of G.IfR
is a field of characteristic zero this yields alternative proofs of
the exactness of the Schneider-Stuhler resolution and of the
Zelevinski conjecture for smooth G-representations generated by
their I-invariants. In general, it gives a description of the
derived category of H-modules in terms of smooth G-representations
and yields a functor to generalized (?, ?)-modules extending the
constructions of Colmez, Schneider and Vigneras.
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