Exact crossed products: a counter-example revisited
The left side of BC (Baum-Connes) with coefficients “sees” any group as if the group were exact. This talk will indicate how to make a change in the right side of BC with coefficients so that the right side also “sees” any group as if the group were exact. This corrected form of BC with coefficients uses the unique minimal exact intermediate crossed-product. For exact groups (i.e., all groups except the Gromov group) there is no change in BC with coefficients. In the corrected form of BC with coefficients the Gromov group acting on the coefficient algebra obtained from an expander is not a counter-example. Thus at the present time (June, 2013) there is no known counter-example to the corrected form of BC with coefficients. The above is joint work with E. Kirchberg and R. Willett. This work is based on — and inspired by — a result of R. Willett and G. Yu.