19Kxx $K$-theory and operator algebras See mainly

{ 46L80, and also 46M20}
19K14  $K_0$ as an ordered group, traces
19K33  EXT and $K$-homology, See also {55N22}
19K35  Kasparov theory ($KK$-theory), See also {58G12}
19K56  Index theory, See also {58G12}
19K99  None of the above but in this section