Geodesic
THE UNITAL EXT-GROUPS AND CLASSIFICATION OF C*-ALGEBRAS
Glasgow mathematical journal, Tome 62 (2020) no. 1, pp. 201-231

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DOI

The semigroups of unital extensions of separable C*-algebras come in two flavours: a strong and a weak version. By the unital Ext-groups, we mean the groups of invertible elements in these semigroups. We use the unital Ext-groups to obtain K-theoretic classification of both unital and non-unital extensions of C*-algebras, and in particular we obtain a complete K-theoretic classification of full extensions of UCT Kirchberg algebras by stable AF algebras. 
GABE, JAMES; RUIZ, EFREN. THE UNITAL EXT-GROUPS AND CLASSIFICATION OF C*-ALGEBRAS. Glasgow mathematical journal, Tome 62 (2020) no. 1, pp. 201-231. doi: 10.1017/S0017089519000053
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     title = {THE {UNITAL} {EXT-GROUPS} {AND} {CLASSIFICATION} {OF} {C*-ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {201--231},
     year = {2020},
     volume = {62},
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     doi = {10.1017/S0017089519000053},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000053/}
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