Coefficient Systems on the Bruhat-Tits Building and Pro-$p$ Iwahori-Hecke Modules 1HFMW and the basic components of

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Coefficient Systems on the Bruhat-Tits Building and Pro-$p$ Iwahori-Hecke Modules 1HFMW and the basic components ofLet 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