CIRCLE ACTIONS ON UHF-ABSORBING C*-ALGEBRAS

We study circle actions with the Rokhlin property, in relation to their restrictions to finite subgroups. We construct examples showing the following: the restriction of a circle action with the Rokhlin property (even on a real rank zero C*-algebra), need not have the Rokhlin property; and even if every restriction of a given circle action has the Rokhlin property, the circle action itself need not have it. As a positive result, we show that the restriction of a circle action with the Rokhlin property to the subgroup Z(n) has the Rokhlin property if the underlying algebra absorbs M-n infinity. The condition on the algebra is also necessary in most cases of interest. Despite the fact that there are no circle actions with the Rokhlin property on UHF-algebras, we construct many such actions on certain UHF-absorbing simple AT-algebras. Additionally, we show that circle actions with the Rokhlin property on O-2-absorbing C*-algebras are generic, in a suitable sense.