The question of whether a right Hilbert bimodule admits a noncommutative frame bundle - i.e, a C*-algebraic noncommutative principal bundle with which the right Hilbert bimodule is associated via some fundamental representation - is both pivotal and difficult. In this paper, we contribute to this topic by providing an axiomatic characterization of a right Hilbert bimodule, let's say M, that ensures the existence of a unique (up to isomorphism) free C*-dynamical system (A_M,SO(n),α_M) with the property that its associated noncommutative vector bundle, with respect to the standard representation of SO(n), is isomorphic to M. Our approach is inspired by potential applications in noncommutative Riemannian spin geometry.

The author wishes to express his thanks to Ludwik Dabrowski, Karl-Hermann Neeb, and Sergey Neshveyev, for helpful conversations and correspondence, and he especially thanks Kay Schwieger for numerous technical conversations over the last several years that have indelibly shaped this work. The author also thanks the anonymous referee for valuable suggestions that helped improve the exposition.