I will begin by discussing Cones' classification of automorphisms of the hyperfinite II_1 factor R and its subsequent generalisations (e.g. group actions and actions of unitary fusion categories).
I will then switch to the C*-setting and explain the new obstructions that occur (spoiler: algebraic K_1) and the result of adapting the von Neumann constructions to the C*-setting (spoiler: different descriptions of R lead to different classifiable C*-algebras).
The talk is based on joint work with Sergio Giron Pacheco.
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