  Schneider-Stuhler and Vigneras have used cosheaves on the affine Bruhat-Tits
building to construct natural finite type projective resolutions for admissible
representations of reductive p-adic groups in characteristic not equal to p. We
use a system of idempotent endomorphisms of a representation with certain
properties to construct a cosheaf and a sheaf on the building. We establish
that these are acyclic and compute homology and cohomology with these
coefficients. This implies Bernstein's result that certain subcategories of the
category of representations are Serre subcategories. Furthermore, we also get
results for convex subcomplexes of the building. Following work of Korman, this
leads to trace formulas for admissible representations.
