Owning a card

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Lets say I am playing against a good friend of mine and I lend him one of my goblin deck.

He then cast Increasing Vengeance from  his graveyard using its flashback ability to copy whatever.

I am play a red/blue spell deck.

Can I cast Innistrad's Runic Repetition targeting the Vengeance since I tecnically "own" the card or the "ownership" of the card depend on who starting playing with their respective deck?

I guess this is not a legal move but I haven't found any rules about the "ownership" of cards to confirm it. 

Thank You. 
proud member of the 2011 community team