  We describe a new kludge scheme to model the dynamics of generic
extreme-mass-ratio inspirals (EMRIs; stellar compact objects spiraling into a
spinning supermassive black hole) and their gravitational-wave emission. The
Chimera scheme is a hybrid method that combines tools from different
approximation techniques in General Relativity: (i) A multipolar,
post-Minkowskian expansion for the far-zone metric perturbation (the
gravitational waveforms) and for the local prescription of the self-force; (ii)
a post-Newtonian expansion for the computation of the multipole moments in
terms of the trajectories; and (iii) a BH perturbation theory expansion when
treating the trajectories as a sequence of self-adjusting Kerr geodesics. The
EMRI trajectory is made out of Kerr geodesic fragments joined via the method of
osculating elements as dictated by the multipolar post-Minkowskian
radiation-reaction prescription. We implemented the proper coordinate mapping
between Boyer-Lindquist coordinates, associated with the Kerr geodesics, and
harmonic coordinates, associated with the multipolar post-Minkowskian
decomposition. The Chimera scheme is thus a combination of approximations that
can be used to model generic inspirals of systems with extreme to intermediate
mass ratios, and hence, it can provide valuable information for future
space-based gravitational-wave observatories, like LISA, and even for advanced
ground detectors. The local character in time of our multipolar
post-Minkowskian self-force makes this scheme amenable to study the possible
appearance of transient resonances in generic inspirals.
