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We give basic properties of the parabolic induction and coinduction functors associated to R-algebras modelled on the pro-p-Iwahori-Hecke R-algebras HR(G) and HR(M) of a reductive p-adic group G and of a Levi subgroup M when R is a commutative ring. We show that the parabolic induction and coinduction functors are faithful, have left and right adjoints that we determine, respect finitely generated R-modules, and that the induction is a twisted coinduction.

The pro-pIwahori Hecke algebra of a reductivep-adic group, V (parabolic induction)