  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.
