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This paper is a contribution to the general problem of giving an explicit description of the basic locus in the reduction modulo p of Shimura varieties. Motivated by [31] and [25], we classify the cases where the basic locus is (in a natural way) the union of classical Deligne-Lusztig sets associated to Coxeter elements. We show that if this is satisfied, then the Newton strata and Ekedahl-Oort strata have many nice properties.

Basic loci of Coxeter type in Shimura varieties