On conjugacy of maximal abelian subalgebras and the outer automorphism group of the Cuntz algebra

We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of maximal abelian subalgebras in On. In particular, we exhibit an uncountable family of maximal abelian subalgebras, conjugate to the standard maximal abelian subalgebra Dn via Bogolubov automorphisms, that are not inner conjugate to Dn