On the K-theory of boundary C *-algebras of à 2 groups

Abstract

Let Γ be an A 2 subgroup of PGL 3 ( ), where is a local field with residue field of order q . The module of coinvariants C ( ,ℤ) Γ is shown to be finite, where is the projective plane over . If the group Γ is of Tits type and if q ≢ 1 (mod 3) then the exact value of the order of the class [1] K 0 in the K-theory of the (full) crossed product C *-algebra C (Ω) ⋊ Γ is determined, where Ω is the Furstenberg boundary of PGL 3 ( ). For groups of Tits type, this verifies a conjecture of G. Robertson and T. Steger.