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Seismic observations by the space-borne mission \emph{Kepler} have shown thatthe core of red giant stars slows down while evolving, requiring an efficientphysical mechanism to extract angular momentum from the inner layers. Currentstellar evolution codes fail to reproduce the observed rotation rates byseveral orders of magnitude, and predict a drastic spin-up of red giant coresinstead. New efficient mechanisms of angular momentum transport are thusrequired.  In this framework, our aim is to investigate the possibility that mixed modesextract angular momentum from the inner radiative regions of evolved low-massstars. To this end, we consider the Transformed Eulerian Mean (TEM) formalism,introduced by Andrews \& McIntyre (1978), that allows us to consider thecombined effect of both the wave momentum flux in the mean angular momentumequation and the wave heat flux in the mean entropy equation as well as theirinterplay with the meridional circulation.  In radiative layers of evolved low-mass stars, the quasi-adiabaticapproximation, the limit of slow rotation, and the asymptotic regime can beapplied for mixed modes and enable us to establish a prescription for the wavefluxes in the mean equations. The formalism is finally applied to a $1.3M_\odot$ benchmark model, representative of observed CoRoT and \emph{Kepler}oscillating evolved stars.  We show that the influence of the wave heat flux on the mean angular momentumis not negligible and that the overall effect of mixed modes is to extractangular momentum from the innermost region of the star. A quantitative andaccurate estimate requires realistic values of mode amplitudes. This isprovided in a companion paper.

Angular momentum redistribution by mixed modes in evolved low-mass stars. I. Theoretical formalism