So? He's a liar, and the father of lies ... the first sin (if one were to sin in response to that particular temptation) would be to think that satan actually had that ownership, and the authority to give it to anyone.
Indeed, we know that all authority (whether used rightly or abused) comes from God.
From the Holy Gospel, according to St. John:
19:7 The Jews answered him, We have a law, and by our law he ought to die, because he made himself the Son of God.
19:8 When Pilate therefore heard that saying, he was the more afraid;
19:9 And went again into the judgment hall, and saith unto Jesus, Whence art thou? But Jesus gave him no answer.
19:10 Then saith Pilate unto him, Speakest thou not unto me? knowest thou not that I have power to crucify thee, and have power to release thee?
19:11 Jesus answered, Thou couldest have no power at all against me, except it were given thee from above: therefore he that delivered me unto thee hath the greater sin.
19:12 And from thenceforth Pilate sought to release him: but the Jews cried out, saying, If thou let this man go, thou art not Caesar's friend: whosoever maketh himself a king speaketh against Caesar.
"would be to think that satan actually had that ownership, and the authority to give it to anyone."
The "World" does belong to the devil - the pride and glory of worldly civilizations. It was forfeited by man at the fall. And of course he has it by God's permission.
"Do not love the world or the things in the world. If anyone loves the world, the love of the Father is not in him. For all that is in the world-- the desires of the flesh and the desires of the eyes and pride in possessions--is not from the Father but is from the world." - 1st John
Satan is still the "god" of this world...
"And even if our gospel is veiled, it is veiled only to those who are perishing. In their case the god of this world has blinded the minds of the unbelievers, to keep them from seeing the light of the gospel of the glory of Christ, who is the image of God." 2 Cor 4