  We present results from three-dimensional hybrid-kinetic simulations of
Alfv\'enic turbulence in a high-beta, collisionless plasma. The key feature of
such turbulence is the interplay between local wave--wave interactions between
the fluctuations in the cascade and the non-local wave-particle interactions
associated with kinetic micro-instabilities driven by anisotropy in the thermal
pressure (namely, firehose, mirror, and ion-cyclotron). We present theoretical
estimates for, and calculate directly from the simulations, the effective
collisionality and plasma viscosity in pressure-anisotropic high-beta
turbulence, demonstrating that, for strong Alfv\'enic turbulence, the effective
parallel-viscous scale is comparable to the driving scale of the cascade. Below
this scale, the kinetic-energy spectrum indicates an Alfv\'enic cascade with a
slope steeper than $-5/3$ due to the anisotropic viscous stress. The
magnetic-energy spectrum is shallower than $-5/3$ near the ion-Larmor scale due
to fluctuations produced by the firehose instability. Most of the cascade
energy (80-90%) is dissipated as ion heating through a combination of Landau
damping and anisotropic viscous heating. Our results have implications for
models of particle heating in low-luminosity accretion onto supermassive black
holes, the effective viscosity of the intracluster medium, and the
interpretation of near-Earth solar-wind observations.
