  We set up a framework of 2-Hilbert bundles, which allows to rigorously define
the "stringor bundle", a higher differential geometric object anticipated by
Stolz and Teichner in an unpublished preprint about 20 years ago. Our framework
includes an associated bundle construction, allowing us to associate a
2-Hilbert bundle with a principal 2-bundle and a unitary representation of its
structure 2-group. We prove that the Stolz-Teichner stringor bundle is
canonically isomorphic to the 2-Hilbert bundle obtained from applying our
associated bundle construction to a string structure on a manifold and the
stringor representation of the string 2-group that we discovered in earlier
work. This establishes a perfect analogy to spin manifolds, representations of
the spin groups, and spinor bundles.
