Embedding of continuous fields of C*-algebras in the Cuntz algebra O2

In a separate pager, it is proved that any separable exact C*-algebra is isomorphic to a subalgebra of the Cuntz algebra O-2. Here, we prove that this embedding is continuous in the following sense. If A is a continuous field of C*-algebras over a compact manifold or finite CW complex X with fiber A(x) over re X, such that the algebra of continuous sections of A is separable and exact, then there is a family of injective homomorphisms phi(x) : A(x) --> CO2 such that for every continuous section a of A the function x bar right arrow phi(x)(a(x)) is continuous. Moreover, one can say something about the modulus of continuity of the functions x bar right arrow phi(x)(a(x)) in terms of the structure of the continuous field. In particular, we show that the continuous field theta bar right arrow A(0) of rotation algebras possesses unital embeddings phi(0) in O-2 such that the standard unitary generators u(theta) and nu(theta) satisfy max(//phi(01)(u(theta(1))) - phi(02)(u(theta(2)))//, //phi(01)(nu(theta(1))) - phi(02)(nu(theta(2)))//) less than or equal to C/theta(1) -theta(2)/(1/2) for some constant C.