  In this work we introduce and analyze a novel Hybrid High-Order method for
the steady incompressible Navier-Stokes equations. The proposed method is
inf-sup stable on general polyhedral meshes, supports arbitrary approximation
orders, and is (relatively) inexpensive thanks to the possibility of statically
condensing a subset of the unknowns at each nonlinear iteration. We show under
general assumptions the existence of a discrete solution, which is also unique
provided a data smallness condition is verified. Using a compactness argument,
we prove convergence of the sequence of discrete solutions to minimal
regularity exact solutions for general data. For more regular solutions, we
prove optimal convergence rates for the energy-norm of the velocity and the
$L^2$-norm of the pressure under a standard data smallness assumption. More
precisely, when polynomials of degree $k\ge 0$ at mesh elements and faces are
used, both quantities are proved to converge as $h^{k+1}$ (with $h$ denoting
the meshsize).
