I understand the traditional theology of omnipotence to be that God can do anything He wills, and that his omnipotence is thereby limited to His nature. In other words, saying that God can do anything does not imply that He can lie or sin. For example:
God is all-powerful and able to do whatever he wills. Since his will is limited by his nature, God can do everything that is in harmony with his perfections. – Thiessen
The best proof texts for this seem to be Hebrews 6:18 and 2 Timothy 2:13. However, based on a debate with a friend, I asked this question on Biblical Hermeneutics SE, and got an answer that surprised me:
According to the answer, Hebrews 6:18 does not necessarily mean that God cannot lie - only that He won't.
So this leads me to a question: What is the Biblical basis for the doctrine that God's omnipotence means that he cannot act against his nature? Would it perhaps be more correct to say that he will not act against his nature?