  In this paper, we describe a geometric setting for higher-order lagrangian
problems on Lie groups. Using left-trivialization of the higher-order tangent
bundle of a Lie group and an adaptation of the classical Skinner-Rusk
formalism, we deduce an intrinsic framework for this type of dynamical systems.
Interesting applications as, for instance, a geometric derivation of the
higher-order Euler-Poincar\'e equations, optimal control of underactuated
control systems whose configuration space is a Lie group are shown, among
others, along the paper.
