algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety variety of Borel subgroups; Langlands conjecture; irreducible representations of reductive p-adic groups; reductive algebraic group; Hecke algebra; Iwahori-Matsumoto algebra; affine Weyl group; equivariant K-homology; equivariant K-cohomology 