Can gravity do what Higgs does?

Conformally invariant model unifying gravity with the Standard Model is proposed. It is based on the observation that the conformal factor couples to matter fields analogously as the Higgs field does so for the proper choice of coupling parameters it can cancel divergences connected with longitudinal boson exchange. The criteria of stability, renormalizability and proper Einsteinian limit suggest that higher derivative terms are necessary in the gravitational sector. This introduces one new parameter but two old parameters of the Higgs potential are redundant due to unification. The Planck mass becomes a dynamical parameter characterizing gravitational background in accordance with Mach's philosophy. Cosmological constant appears in a natural way. (author). 18 refs