Let B be a separable stable C*-algebra. Then B is said to have the corona factorization property if every (norm-) full projection in M(B) (the multiplier algebra of B) is Murray-von Neumann equivalent to the unit of M(B).

The corona factorization property originally arose through the study of absorbing extensions (which are of interest in KK-theory, as well as the stable existence and stable uniqueness theorems of classification theory). This subject has subsequently been shown to be much connected to the structure and classification of C*-algebras (e.g. stability theory, the classification of nonsimple C*-algebras, classification of nonsimple C*-algebras coming from graphs and dynamical systems, etc.)

This talk is a sample of selected results about the corona factorization property with some connections to other subjects. This talk is meant to be accessible to a wide audience, and the emphasis is on making what I say understandable, rather than on mentioning a great many topics.