(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 1999)
We consider th C^*-algebra W H(R^n,P) of the multivariable Wiener-Hopf operators associated with a polyhedral cone in R^n and the extension 0 → K → W H(R^n,P) → W H (R^n,P)/K → 0. The main theorem states that if P satisfies suitable geometric conditions (satisfied, e.g., for all simplicial cones and the cones in R^n,n ≤ 3), then K_*(W H(R^n,P)) = (0,0); K_*(W H(R^n,P)/K) = (0,Z) and that the index map is an isomorphism. In the cource of the proof we construct a Fredholm operator in W H(R^n, P) with an index 1. The proof is inductive and uses the Mayer-Vietoris exact sequence and the standart six term exact sequence in K-theory.