Pretty much the ring can synthesize Kryptonite, and this isn't the sliver Batman carries in his pouch, or the rock Luthor has on a chain. He throws up a SUN sized ever expanding kryptonite force field that blocks, and then completely surrounds him, and then proceeds to crush Superman under, and inside it. While simultaneously blocking out the sun, syphoning oxygen, and piercing him with endless barrage of kryptonite shards of hard light, he can't even punch back at them, or the crushing mass.
The power level reflects Jordan's will, so as long as he's charged and willing, he can pretty much shut him down ........................... That is, as long as the power lasts.
Once that power runs out though, if he GL hasn't killed him, LOL he's so dead.
Add Parallax power = willingness to kill. and it's over.
So yes GL (Jordan) can but won't.
As Parallax can and would!