Wiener-Hopf Operators on Ordered Homogeneous Spaces, I

The C*-algebra WP of Wiener-Hopf operators related to an ordered homogeneous space G/H is shown to be the homomorphic image of a groupoid C*-algebra. To obtain this groupoid C*-algebra we construct an ordered compactification of G/H. The regularity of this compactification permits to show that WP contains the ideal of compact operators.