l-Adic etale cohomology of Shimura varieties of Hodge type with non-trivial coefficients

Let (G, X) be a Shimura datum of Hodge type. Let p be an odd prime such that G(Qp) splits after a tamely ramified extension and p inverted iota vertical bar pi(1)(G(der))vertical bar. Under some mild additional assumptions that are satisfied if the associated Shimura variety is proper and G(Qp) is either unramified or residually split, weprove the generalisation of Mantovan's formula for the l-adic cohomology of the associated Shimura variety. On the way we derive some new results about the geometry of the Newton stratification of the reduction modulo p of the Kisin-Pappas integral model.