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We used new ALMA $^{13}$CO and C$^{18}$O(3-2) observations obtained at highangular resolution ($\sim$0.2") together with previous CO(3-2) and (6-5) ALMAdata and continuum maps at 1.3 and 0.8 mm in order to determine the gasproperties (temperature, density, and kinematics) in the cavity and to a lesserextent in the outer disk of GG Tau A, the prototype of a young triple T Tauristar that is surrounded by a massive and extended Keplerian outer disk. Bydeprojecting, we studied the radial and azimuthal gas distribution and itskinematics. We also applied a new method to improve the deconvolution of the COdata and in particular better quantify the emission from gas inside the cavity.We perform local and nonlocal thermodynamic equilibrium studies in order todetermine the excitation conditions and relevant physical parameters inside thering and in the central cavity. Residual emission after removing a smooth-diskmodel indicates unresolved structures at our angular resolution, probably inthe form of irregular rings or spirals. The outer disk is cold, with atemperature $<20$ K beyond 250 au that drops quickly (r$^{-1}$). The kinematicsof the gas inside the cavity reveals infall motions at about 10% of theKeplerian speed. We derive the amount of gas in the cavity, and find that thebrightest clumps, which contain about 10% of this mass, have kinetictemperatures 40$-$80 K, CO column densities of a few 10$^{17}$ cm$^{-2}$, andH$_2$ densities around 10$^7$ cm$^{-3}$. Although the gas in the cavity is onlya small fraction of the disk mass, the mass accretion rate throughout thecavity is comparable to or higher than the stellar accretion rate. It isaccordingly sufficient to sustain the circumstellar disks on a long timescale.

GG Tau A: gas properties and dynamics from the cavity to the outer disk