How does Sir Gawain demonstrate nobility in Sir Gawain and the Green Knight?

Sir Gawain demonstrates his nobility in several ways. In the very beginning of the novel, when the Green Knight storms King Arthur's castle, Gawain volunteers to take up the challenge the Green Knight offers. King Arthur is more than ready take on the Green Knight's challenge, but Gawain wishes to go in his place because he is of lesser value to the court than King Arthur is: 

'I am the weakest, I know, and of wit feeblest.

least worth the loss of my life, who’d learn the truth.

Only inasmuch as you are my uncle, am I praised:

No bounty but your blood in my body I know.

And since this thing is folly and naught to you falls,

and I have asked it of you first, grant it to me;

and if my cry be not comely, let this court be free

of blame.’

Gawain knows he will most likely be killed by the Green Knight, but nonetheless takes up this challenge because it would not be right for the King to die for such a foolish cause.

Later in the novel Sir Gawain further shows his nobility by striving to find the Green Knight on the day they had agreed to meet. It is stated that, while on his journey to find the Green Chapel, Gawain battles his way though the woods and survives near deadly cold weather. It is seen as noble that Gawain deals with all this valiantly and with almost no complaints.

When he is finally able to rest for a while at the castle of Bertilak, he is tempted by Bertilak's wife:

'. . . my lord and his lords are far off faring,

other knights are abed, and my ladies also,

the door drawn and shut with a strong hasp.

And since I have in this house him who all like,

I shall work my time well, while it lasts,

                    with a tale.

          Your are welcome to my body,

          Your pleasure to take all;

          I must by necessity

          your servant be, and shall.’

Although Gawain is tempted to have an affair with Bertilak's wife on three separate occasions, he never gives in, and this restraint is seen as both noble, and the epitome of Gawain's virtuous nature. While tempting Gawain Bertilak's wife gives him a few kisses and Gawain is noble enough to tell Bertilak of this. As well, Gawain "returns" the kisses to Bertilak. 

Then, when Gawain finally heads directly to the Green Chapel, he is advised one last time to turn back but Gawain nobly goes forth thinking he will most certainly die. And, when Gawain kneels to take the blow from the Green Knight's ax, he flinches the first time, but the second time he takes the blow without recoiling at all. 

Overall, Gawain is mostly just noble in his abilities to face the things he fears the most and keep his word.