  Seismic observations by the space-borne mission \emph{Kepler} have shown that
the core of red giant stars slows down while evolving, requiring an efficient
physical mechanism to extract angular momentum from the inner layers. Current
stellar evolution codes fail to reproduce the observed rotation rates by
several orders of magnitude, and predict a drastic spin-up of red giant cores
instead. New efficient mechanisms of angular momentum transport are thus
required.
  In this framework, our aim is to investigate the possibility that mixed modes
extract angular momentum from the inner radiative regions of evolved low-mass
stars. To this end, we consider the Transformed Eulerian Mean (TEM) formalism,
introduced by Andrews \& McIntyre (1978), that allows us to consider the
combined effect of both the wave momentum flux in the mean angular momentum
equation and the wave heat flux in the mean entropy equation as well as their
interplay with the meridional circulation.
  In radiative layers of evolved low-mass stars, the quasi-adiabatic
approximation, the limit of slow rotation, and the asymptotic regime can be
applied for mixed modes and enable us to establish a prescription for the wave
fluxes in the mean equations. The formalism is finally applied to a $1.3
M_\odot$ 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 momentum
is not negligible and that the overall effect of mixed modes is to extract
angular momentum from the innermost region of the star. A quantitative and
accurate estimate requires realistic values of mode amplitudes. This is
provided in a companion paper.
