  Let $(\mathsf{G},\mathsf{X})$ be a Shimura datum of Hodge type. Let $p$ be an
odd prime such that $\mathsf{G}_{\mathbb{Q}_p}$ splits after a tamely ramified
extension and $p\nmid |\pi_1(\mathsf{G}^{\rm der})|$. Under some mild
additional assumptions that are satisfied if the associated Shimura variety is
proper and $\mathsf{G}_{\mathbb{Q}_p}$ is either unramified or residually
split, we prove 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.
