Inner products of deep level Deligne--Lusztig representations of Coxeter type

In this article we prove orthogonality relations for deep level Deligne--Lusztig varieties of Coxeter type, attached to a reductive group over a local non-archimedean field, which splits over an unramified extension. This extends results of Dudas and the first author, where the quasi-split case was handled. This allows to construct new irreducible representations of parahoric subgroups of p-adic groups.