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In this paper we prove some orthogonality relations for representationsarising from deep level Deligne--Lusztig schemes of Coxeter type. Thisgeneralizes previous results of Lusztig (2004), and of Chan and the secondauthor (2019). Potential applications include the study of unipotentrepresentations arising from such deep level Deligne--Lusztig schemes, as wellas their geometry, in the spirit of the work of Lusztig (1976).

Orthogonality relations for deep level Deligne--Lusztig schemes of Coxeter type