  In this paper, we investigate the astrophysical processes of stellar-mass
black holes (sMBHs) embedded in advection-dominated accretion flows (ADAFs) of
supermassive black holes (SMBHs) in low-luminosity active galactic nuclei
(AGNs). The sMBH is undergoing Bondi accretion at a rate lower than the SMBH.
Outflows from the sMBH-ADAF dynamically interact with their surroundings and
form a cavity inside the SMBH-ADAF, thereby quenching the accretion onto the
SMBH. Rejuvenation of the Bondi accretion is rapidly done by turbulence. These
processes give rise to quasi-periodic episodes of sMBH activities and create
flickerings from relativistic jets developed by the Blandford-Znajek mechanism
if the sMBH is maximally rotating. Accumulating successive sMBH-outflows
trigger viscous instability of the SMBH-ADAF, leading to a flare following a
series of flickerings. Recently, the similarity of near-infrared flare's orbits
has been found by GRAVITY/VLTI astrometric observations of Sgr A$\!^{*}$: their
loci during the last 4-years consist of a ring in agreement with the
well-determined SMBH mass. We apply the present model to Sgr A$\!^{*}$, which
shows quasi-periodic flickerings. A SMBHH of $\sim 40 M_{\odot}$ is preferred
orbiting around the central SMBH of Sgr A$\!^{*}$ from fitting radio to X-ray
continuum. Such an extreme mass ratio inspiraling (EMRI) provides an excellent
laboratory for LISA, Taiji and Tianqin detection of mHz gravitational waves
with strains of $\sim 10^{-17}$, as well as their polarization.

High Energy Astrophysical Phenomena;Astrophysics of Galaxies