Ck,αCk,α-regularity of solutions to quasilinear equations structured on Hörmander’s vector fields

For a linear nonvariational operator structured on smooth Hörmander’s vector fields, with Hölder continuous coefficients, we prove a regularity result in the scale of CXk,α spaces. We deduce an analogous regularity result for nonvariational degenerate quasilinear equations.