  For all transcendental parameters, the irrational rotation algebra is shown
to contain infinitely many C*-subalgebras satisfying the following properties.
Each subalgebra is isomorphic to a direct sum of two matrix algebras of the
same (perfect square) dimension; the Fourier transform maps each summand onto
the other; the corresponding unit projection is approximately central; the
compressions of the canonical generators of the irrational rotation algebra are
approximately contained in the subalgebra.
