We aim to unveil the observational imprint of physical mechanisms that govern planetary formation in the young, multiple system GG Tau A. We present ALMA observations of $^{12}$CO and $^{13}$CO 3-2 and 0.9 mm continuum emission with 0.35 resolution. The $^{12}$CO 3-2 emission, found within the cavity of the circumternary dust ring (at radius $< 180$ AU) where no $^{13}$CO emission is detected, confirms the presence of CO gas near the circumstellar disk of GG Tau Aa. The outer disk and the recently detected hot spot lying at the outer edge of the dust ring are mapped both in $^{12}$CO and $^{13}$CO. The gas emission in the outer disk can be radially decomposed as a series of slightly overlapping Gaussian rings, suggesting the presence of unresolved gaps or dips. The dip closest to the disk center lies at a radius very close to the hot spot location at $sim250-260$~AU. The CO excitation conditions indicate that the outer disk remains in the shadow of the ring. The hot spot probably results from local heating processes. The two latter points reinforce the hypothesis that the hot spot is created by an embedded proto-planet shepherding the outer disk.
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