To display a false front or use dishonest advertising to sell inferior or different goods; misrepresentation.

这家店挂羊头卖狗肉，广告上说是真丝，卖的却是化纤。

To carry out wicked or selfish deeds under the banner of virtue or noble principles.

他表面上提倡慈善，实际却是挂羊头卖狗肉，把捐款都私吞了。