Completely bounded subcontexts of a Morita context of unital C∗-algebras

We answer a question of Blecher--Muhly--Paulsen, identifying topological invariants for cb Morita equivalences of holomorphic cross-section algebras. Previously, given a certain subcontext of a Morita context of n-homogeneous C∗-algebras whose spectrum T is an annulus, the norm of a lifting of 1A of a given subalgebra A was estimated by conformal and bundle invariants. We give a generalization in which T is a bordered Riemann surface. In doing so, we develop a sufficient criterion for when a unital completely bounded Morita equivalence can be factored into a similarity and a strong Morita equivalence.