2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67683This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].30 pages. Any comments are welcome. Minor changesOperator Algebras46L05,06,10text