  Let V be a finite dimensional real Euclidean Jordan algebra with the identity
element 1. Let Q be the closed convex cone of squares. We show that the Wiener-
Hopf compactification of Q is the interval (1-Q) \cap (-1+Q). As a consequence,
we deduce that the K-groups of the Wiener-Hopf C^{*}-algebra associated to Q
are trivial.
