The knights of the round table express their solidarity by wearing a green girdle as gawain does. why does gawain wear the green girdle?

In the beginning, Sir Gawain was given the green girdle by his lover, Lady Bertilak, as a token of their 'love.' She also told him the girdle would make him invincible. When he fought with her husband, Bertilak, he was supposed to win and give him the girdle, however, he failed in doing that. Therefore he continued wearing the girdle as a sign of his shame and failure. His fellow knights felt very compassionate and wanted to show their support for him by wearing a green girdle as well.