It has something to do with him and the green knight.
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Arthur doesn't have a very large part in this story. We initially meet him in the beginning when the Green Knight crashes his celebratory feast durung the holidays. Because he is a good King and leader, Arthur steps forward to accept the Green Knights challenge..... Gawain steps in.
At the end of the story, Arthur wears a green girdle in honor of Gawain's accomplishments.