The Rohlin Property for Shifts on UHF Algebras and Automorphisms of Cuntz Algebras

We show that the shift on the UHF algebraMn∞has the Rohlin property for any oddn(hence, by Brotteliet al.(The crossed product of a UHF algebra by a shift,Ergodic Theory Dynam. Systems13(1993), 615–626), for anyn=2, 3, …), and that any automorphismαof the Cuntz algebraOn(n<∞) has the Rohlin property ifαmis outer for anym≠0.