What few Green Lantern comics I own are all from Kyle Rayner's stretch as the sole ring-bearer. The only one I bought at the time it came out was the final issue, for reasons I can no longer recall. That ends with him decapitating Major Force and sending his head floating into the void. Then Kyle decides to go into space.
Pretty sure the next time he pops up is Green Lantern: Rebirth, where he managed to not get snuffed by Geoff (goddamnit, I spelled it "Geoof" on the first try again) Johns, against all expectations.
The others are from the stretch when Kyle tapped into all the power Hal left behind when he reignited the Sun during Final Night, becoming rather godlike in the process. Kyle manages to not try and reboot the entire universe, but does gradually extend his abilities. On a grand scale, he travels to an alien world he visited previously, still torn apart by conflict, and simply makes violence impossible. Oh, people can try, but any attempt, from using a laser tank to a rock is thwarted by him. The idea seemingly being that, with killing or harming all their adversaries off the table, the sides will have to learn to co-exist.
On smaller scales, he reignites his then-girlfriend Jade's inherent powers, so she no longer has to rely on a power ring. He also tracks down his father, who was apparently an intelligence agent who wanted out of the life, and is so skilled, he covered his tracks beyond the ability of anyone Kyle knows to track him down.
Kyle ultimately chooses to recreate the Central Power Battery, which somehow creates a bunch of new Guardians. So we get a whole new batch of little blue morons. That was after Superman gave him the old, "we can't do too much for humanity or we stifle their potential," speech, and Kyle debating whether to stop Hal Jordan from going down his dark path. So he was going to mess with time, just a little.
Kyle's presented as still inexperienced in some ways. Still only touching the surface of what he can do with these powers. But also wise enough to know when to ask questions. Ask Hal if he wants Kyle to change the past (unsurprisingly, Hal has an active role in this story.) Ask Alan Scott for his perspective on having this much power inside. And when he renounces it, wise enough to make some changes to his ring to address certain problems he's had in the past, like the ring getting taken away from him, or running out of power entirely.
It's an OK storyline, although he creates a new costume that's kind of hideous. Way too much white, almost no green. When he goes back to just being a Green Lantern, he creates the costume I remember seeing described as looking like a sneaker. I can see what they mean, but I like it all right. That may be because it was the one he wore during Joe Kelly's Obsidian Age storyline, which I was rather fond of.
