Automorphisms of C∗-algebra bundles

AbstractLet B be a unital C∗-algebra and A = Γ(E) be the C∗-algebra of sections of a bundle over the separable compact space X with fibre B and structure group Inn B. If B is the quotient of an AW∗-algebra, then an exact sequence: 0 → Inn A → PInn A →η H2(X, G), where PInn A is the group of pointwise inner automorphisms of A and G=H°(Z(B)^, Z) is obtained. The map η is onto whenever A = C(X, B) and B is the quotient of a purely infinite AW∗-algebra. An essential part of the analysis is the result that Ad: U(B) → Inn B is a fibre bundle if and only if the space of inner derivations of B is norm closed. These results extend and clarify previous joint work with I. Raeburn (Indiana Univ. Math. J. 29 (1980), 799)