  We construct a new class of stable vector bundles suitable for heterotic
string compactifications. Using these we describe a novel way to derive the
fermionic matter content of the Standard Model from the heterotic string. For
this we compactify on an elliptically fibered Calabi-Yau threefold X with two
sections, the B-fibration, a variant of the ordinary Weierstrass fibration,
which allows X to carry a free involution. We construct rank five vector
bundles, invariant under this involution, such that turning on a Wilson line we
obtain the Standard Model gauge group and find various three generation models.
This rank five bundle is derived from a stable rank four bundle that arises as
an extension of bundles pulled-back from the base and twisted by suitable line
bundles. We also give an account of various previous results and put the
present construction into perspective.
