  Fast radio bursts (FRBs) are luminous millisecond-duration radio pulses with
extragalactic origin, which were discovered more than a decade ago. Despite the
numerous samples, the physical origin of FRBs remains poorly understood. FRBs
have been thought to originate from young magnetars or accreting compact
objects (COs). Massive stars or COs are predicted to be embedded in the
accretion disks of active galactic nuclei (AGNs). The dense disk absorbs FRBs
severely, making them difficult to observe. However, progenitors ejecta or
outflow feedback from the accreting COs interact with the disk material to form
a cavity. The existence of the cavity can reduce the absorption by the dense
disk materials, making FRBs escape. Here we investigate the production and
propagation of FRBs in AGN disks and find that the AGN environments lead to the
following unique observational properties, which can be verified in future
observation. First, the dense material in the disk can cause large dispersion
measure (DM) and rotation measure (RM). Second, the toroidal magnetic field in
the AGN disk can cause Faraday conversion. Third, during the shock breakout, DM
and RM show non-power-law evolution patterns over time. Fourth, for
accreting-powered models, higher accretion rates lead to more bright bursts in
AGN disks, accounting for up to 1% of total bright repeating FRBs.
