The Oka principle in complex geometry asserts that continuous structures in a variety of contexts, including vector bundles on polynomially convex sets, carry unique holomorphic structures, up to isomorphism. The Oka principle fits naturally into K-theory, and it has long been proposed as a mechanism to understand cases of the Baum-Connes conjecture. I shall explain how in the case of real reductive groups it may be combined with the Langlands classification to produce an interesting new perspective on the Connes-Kasparov isomorphism. This is joint work with Jacob Bradd.
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