What is the ruling on money acquired from the AdSense advertising program if one repents from it after receiving the amount? And is it obligatory to cash the check, or is it sufficient to destroy it? And how can one expiate for the illicit advertisements that were displayed on the website?

Expiation for the sin resulting from displaying impermissible advertisements is achieved through repentance and by ridding oneself of ill-gotten gains. This is done by estimating the proportion of impermissible advertisements out of the total advertisements displayed, and then giving away that proportion of the money earned. As for money earned from permissible advertisements, there is no sin in it.