  Interactions and particles in the standard model are characterized by the
action of internal and external symmetry groups. The four symmetry regimes
involved are related to each other in the context of induced group
representations. In addition to Wigner's induced representations of external
Poincar\'e group operations, parametrized by energy-momenta, and the induced
internal hyperisospin representations, parametrized by the standard model Higgs
field, the external operations, including the Lorentz group, can be considered
to be induced also by representations of the internal hypercharge-isospin
group. In such an interpretation nonlinear spacetime is parametrized by the
orbits of the internal action group in the external action group.
