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Zygarde's relation to Kalos is never fully elaborated upon, they killed Pokemon Z, or XY2 or whatever it was supposed to be.
The SM Pokedex calls it stronger than Xerneas/Yveltal, but we never actually see this take place in the story. Unlike say Rayquaza, which appears to stop Kyogre/Groudon in Emerald and has an in-battle ability that corresponds to its legend (Air Lock cancels out weather abilities). Aura Break exists, but Zygarde loses that when it transforms sadly.