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Work of Bezrukavnikov--Kazhdan--Varshavsky uses an equivariant system oftrivial idempotents of Moy--Prasad groups to obtain an Euler--Poincar\'eformula for the r--depth Bernstein projector. We establish an Euler--Poincar\'eformula for the projector to an individual depth zero Bernstein component interms of an equivariant system of Peter--Weyl idempotents of parahoricsubgroups P associated to a block of the reductive quotient of P.

An Euler-Poincar\'e formula for depth zero Bernstein projector