  We extend the ab initio no-core shell model/resonating-group method to
include three-nucleon (3N) interactions for the description of nucleon-nucleus
collisions. We outline the formalism, give algebraic expressions for the
3N-force integration kernels, and discuss computational aspects of two
alternative implementations. The extended theoretical framework is then applied
to nucleon-4He scattering using similarity-renormalization-group (SRG) evolved
nucleon-nucleon plus three-nucleon potentials derived from chiral effective
field theory. We analyze the convergence properties of the calculated phase
shifts and explore their dependence upon the SRG evolution parameter. We
include up to six excited states of the 4He target and find significant effects
from the inclusion of the chiral 3N force, e.g., it enhances the spin-orbit
splitting between the 3/2- and 1/2- resonances and leads to an improved
agreement with the phase shifts obtained from an accurate R-matrix analysis of
the five-nucleon experimental data. We find remarkably good agreement with
measured differential cross sections at various energies, while analyzing
powers manifest larger deviations from experiment for certain energies and
angles.
