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Let A and B be arbitrary C*-algebras, we prove that the existence of a Hilbert Aï¿½??B-bimodule of finite index ensures that the WEP, QWEP, and LLP along with other finite-dimensional approximation properties such as CBAP and (S)OAP are shared by A and B. For this, we first study the stability of the WEP, QWEP, and LLP under Morita equivalence of C*-algebras. We present examples of Hilbert Aï¿½??B-bimodules,which are not of finite index, while such properties are shared between A and B. To this end, we study twisted crossed products by amenable discrete groups.
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