THE EXACT TRACIAL ROKHLIN PROPERTY

It is proved that the noncommutative Fourier transform automorphism sigma of the irrational rotation algebra has the exact tracial Rokhlin property a slightly stronger version of N. Christopher Phillips' tracial Rokhlin property. It essentially means that there are approximately central projections g such that g, sigma(g), sigma(2) (g), sigma(3) (g) are mutually orthogonal and 1-g-sigma(g)-sigma(2)(g)-sigma(3)(g) is a 'small' projection in the sense that it is Murray von Neumann equivalent to a subprojection of any prescribed projection. Consequently, the flip automorphism and the restriction of the Fourier transform to the flip-fixed point subalgebra also have the exact tracial Rokhlin property.