Yes, you leave the ring in place. The crank bolt has a flange behind it so it pulls the crank off when the bolt is backed out.
Self extracting cranks have come into and out of favor over the years. They work fine 99% of the time, but are a royal pain when they don't. Keep yours working well by adding some oil between the bolt and the ring before pulling the crank. This will lubricate the back of the ring where the bolt pushes as it turns.
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