Classification of $\mathcal {O}_\infty $-Stable $C^*$-Algebras (Memoirs of the
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Present a proof of Kirchberg's classification theorem: two separable, nuclear, $\mathcal {O}_\infty $-Stable $C^*$-algebras are stably isomorphic if and only if they are idealrelated KK-equivalent. In particular, this provides a more elementary proof of the Kirchberg–Phillips theorem which is isolated in the paper to increase readability of this important special case.
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