Each Euroland country issues its own banknotes whose origin can be identified by the first letter of the serial number. Greek notes begin with a Y.
Who actually OWNS the banknotes in your wallet or purse? There must be thousands of Greek euro notes outside Greece so, if the Greek National Bank "owns" banknotes issued on its behalf and recalled them via the banks in other Euroland countries would that help? I think not but this question of ownership of banknotes is intriguing.
In time, they would find their way into various banks. I'm not really serious in suggesting this as a solution to Greece's problems. It's just interesting googling "who owns banknotes?"
Interesting question. My banknotes state, "I promise to pay the bearer on demand ..." so they are clearly an IOU of some sort, with an obligation on/admission from the government that I'm owed. So as far as I can see I should be considered the owner until I cash it in somewhere in society, probably by exchanging it for goods or services.