  In the standard model matter fields form complete representations of a grand
unified group whereas Higgs fields belong to incomplete `split' multiplets.
This remarkable fact is naturally explained by `local grand unification' in
higher-dimensional extensions of the standard model. Here, the generations of
matter fields are localized in regions of compact space which are endowed with
a GUT gauge symmetry whereas the Higgs doublets are bulk fields. We realize
local grand unification in the framework of orbifold compactifications of the
heterotic string, and we present an example with SO(10) as a local GUT group,
which leads to the supersymmetric standard model as an effective
four-dimensional theory. We also discuss different orbifold GUT limits and the
unification of gauge and Yukawa couplings.
