  We present a novel Hybrid High-Order (HHO) discretization of fourth-order
elliptic problems arising from the mechanical modeling of the bending behavior
of Kirchhoff-Love plates, including the biharmonic equation as a particular
case. The proposed HHO method supports arbitrary approximation orders on
general polygonal meshes, and reproduces the key mechanical equilibrium
relations locally inside each element. When polynomials of degree $k \ge 1$ are
used as unknowns, we prove convergence in $h^{k+1}$ (with $h$ denoting, as
usual, the meshsize) in an energy-like norm. A key ingredient in the proof are
novel approximation results for the energy projector on local polynomial
spaces. Under biharmonic regularity assumptions, a sharp estimate in $h^{k+3}$
is also derived for the $L^2$-norm of the error on the deflection. The
theoretical results are supported by numerical experiments, which additionally
show the robustness of the method with respect to the choice of the
stabilization.
