  The evolution of a linearly-polarized, long-wavelength Alfv\'en wave
--propagating in a collisionless magnetized plasma with a sheared
parallel-directed velocity flow-- is here studied by means of two-dimensional
hybrid Vlasov-Maxwell (HVM) simulations. The unperturbed sheared flow has been
represented by an exact solution of the HVM set of equations (Malara {\it et
al.}, Phys. Rev. E 97, 053212), this avoiding spurious oscillations that would
arise from the non-stationary initial state and inevitably affect the dynamics
of the system. We have considered the evolution of both a small and a moderate
amplitude Alfv\'en wave, in order to separate linear wave-shear flow couplings
from kinetic effects, the latter being more relevant for larger wave
amplitudes. The phase-mixing generated by the shear flow modifies the initial
perturbation, leading to the formation of small-scale transverse fluctuations
at scales comparable with the proton inertial length. By analyzing both the
polarization and group velocity of perturbations in the shear regions, we
identify them as Kinetic Alfv\'en Waves (KAWs). In the moderate amplitude run,
kinetic effects distort the proton distribution function in the shear region.
This leads to the formation of a proton beam, at the Alfv\'en speed and
parallel to the magnetic field. Such a feature, due to the parallel electric
field associated with KAWs, positively compares with solar-wind observations of
suprathermal ions' populations, suggesting that it may be related to the
presence of ion-scales KAW-like fluctuations.
