BERG TECHNIQUE FOR PSEUDO-ACTIONS WITH APPLICATIONS TO AF EMBEDDINGS

Berg's interchange technique is generalized to the context of certain new objects called pseudo-actions. This is used to find a more geometric proof of the Pimsner-Voiculescu theorem on the AF embedding of the irrational rotation algebras. Connections with Berg's original results are briefly examined. Embedding diagrams are introduced to provide a uniform way of describing embeddings of transformation group C*-algebras C(X) times sign bar connected to right Z into AF algebras. Pimsner has classified the transformation group C*-algebras which can be AF embedded. We present a new proof of this result using embedding diagrams and pseudo-actions. The need to calculate the join of an open cover with its iterates under the transformation has been eliminated.