  We propose new mechanism for inflation using classical SU(2) Yang-Mills (YM)
homogeneous and isotropic field non-minimally coupled to gravity via Horndeski
prescription. This is the unique generally and gauge covariant ghost-free YM
theory with the curvature-dependent action leading to second-order gravity and
Yang-Mills field equations. We show that its solution space contains de Sitter
boundary to which the trajectories are attracted for some finite time, ensuring
the robust inflation with a graceful exit. The theory can be generalized to
include the Higgs field leading to two-steps inflationary scenario, in which
the Planck-scale YM-generated inflation naturally prepares the desired initial
conditions for the GUT-scale Higgs inflation.
