Luke 4.5-7: And the devil took him up and showed him all the kingdoms of the world in a moment of time, (6) and said to him, “To you I will give all this authority and their glory, for it has been delivered to me, and I give it to whom I will. (7) If you, then, will worship me, it will all be yours.” (ESV)
In John 8.44 Jesus said the following about the devil, “when he lies, he speaks out of his own character, for he is a liar and the father of lies.” (ESV). So we can know for certain that the proposition the devil made to Jesus in the verses above was built upon lies and deception. The devil asserts that all of the kingdoms of the world are under his authority, but that is not the truth. To whatever extent the devil works his evil in the world, it is because God allows the devil to work in and through the minds of people who choose for themselves to do the devil’s will.
But the devil does not have independent authority over anything. In the beginning of the Book of Job, the devil’s actions are strictly limited by the LORD God. And we can read in chapters 45 and 47 of Isaiah, for example, that the kingdoms of the world, and their actions, are subject to the ultimate authority and plans of the LORD God. So the devil’s temptation was founded upon a lie. He has never at any time been able to do what he promised to Jesus, and the bargain itself was a lie.