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We compute the algebraic K-theory of the Hecke algebra of a reductive p-adicgroup G using the fact that the Farrell-Jones Conjecture is known in thiscontext. The main tool will be the properties of the associated Bruhat-Titsbuilding and an equivariant Atiyah-Hirzebruch spectral sequence. In particularthe projective class group can be written as the colimit of the projectiveclass groups of the compact open subgroups of G.

Recipes to compute the algebraic K-theory of Hecke algebras of reductive p-adic groups