The HESS collaboration recently reported highly significant detection of TeV gamma -rays coincident with Sgr A^* \citepHESS. In the context of other Galactic Center (GC) observations, this points to the following scenario: In the extreme advection-dominated accretion flow (ADAF) regime of the GC black hole (BH), synchrotron radio/sub-mm emission of 100 MeV electrons emanates from an inefficiently radiating turbulent magnetized corona within 20 R_S (Schwarzschild radii) of the GCBH. These electrons are accelerated through second-order Fermi processes by MHD turbulence, as suggested by Liu et al. (2004). Closer to the innermost stable orbit of the ADAF, instabilities and shocks within the flow inject power-law electrons through first-order Fermi acceleration to make synchrotron X-ray flares observed with Chandra, XMM, and INTEGRAL. A subrelativistic MHD wind subtending a 1 sr cone with power > 1037 erg s-1 is driven by the ADAF from the vicinity of the GCBH. As in pulsar powered plerions, electrons are accelerated at the wind termination shock, at > 1016.5 cm from the GCBH, and Compton-scatter the ADAF and the far infra-red (FIR) dust radiation to TeV energies. The synchrotron radiation of these electrons forms the quiescent X-ray source resolved by Chandra. The radio counterpart of this TeV/X-ray plerion, formed when the injected electrons cool on timescales of > 104 yrs, could explain the origin of nonthermal radio emission in the pc-scale bar of the radio nebula Sgr A West.