  We perform relativistic hydrodynamic simulations of the formation and
evolution of AGN cocoons produced by very light powerful jets. We calculate the
intensity maps of the Sunyaev-Zel'dovich (SZ) effect at high frequencies for
the simulated AGN cocoons using the relativistically correct Wright formalism.
Our fully relativistic calculations demonstrate that the contribution from the
high temperature gas (kb Te ~ 100 keV) to the SZ signal from AGN cocoons at
high frequencies is stronger than that from the shocked ambient intercluster
medium owing to the fact that the relativistic spectral functions peak at these
temperature values. We present simulations of the SZ effect from AGN cocoons at
various frequencies, and demonstrate that SZ observations at 217 GHz and at
higher frequencies, such as 857 GHz, will provide us with knowledge about the
dynamically-dominant component of AGN cocoons.
