Automorphic Forms, Cohomology and CAP Representations. The Case GL2 over a Definite Quaternion Algebra

In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group G = GL₂ over a definite quaternion algebra D/Q. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having cohomology in degree 1. The latter ones turn out to be CAP-representations, though G satisfies Strong Multiplicity One.