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In this paper, we investigate the astrophysical processes of stellar-massblack holes (sMBHs) embedded in advection-dominated accretion flows (ADAFs) ofsupermassive 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 andform a cavity inside the SMBH-ADAF, thereby quenching the accretion onto theSMBH. Rejuvenation of the Bondi accretion is rapidly done by turbulence. Theseprocesses give rise to quasi-periodic episodes of sMBH activities and createflickerings from relativistic jets developed by the Blandford-Znajek mechanismif the sMBH is maximally rotating. Accumulating successive sMBH-outflowstrigger viscous instability of the SMBH-ADAF, leading to a flare following aseries of flickerings. Recently, the similarity of near-infrared flare's orbitshas been found by GRAVITY/VLTI astrometric observations of Sgr A$\!^{*}$: theirloci during the last 4-years consist of a ring in agreement with thewell-determined SMBH mass. We apply the present model to Sgr A$\!^{*}$, whichshows quasi-periodic flickerings. A SMBHH of $\sim 40 M_{\odot}$ is preferredorbiting around the central SMBH of Sgr A$\!^{*}$ from fitting radio to X-raycontinuum. Such an extreme mass ratio inspiraling (EMRI) provides an excellentlaboratory for LISA, Taiji and Tianqin detection of mHz gravitational waveswith strains of $\sim 10^{-17}$, as well as their polarization.

Accretion-modified Stars in Accretion Disks of Active Galactic Nuclei: the Low-luminosity Cases and an Application to Sgr A$\!^{*}$