[jeroenhd]

> which entity gives those pieces of paper their value

The USA can print and lend dollars to control the value of the currency on the global marketplace. When trading outside of the USA, people give the bills their value.

You can substitute a suitcase with a million dollars for a suitcase full of gold or a suitcase full of diamonds, or a suitcase full of Pokémon cards. Outside the official banking system, the value of paper money is whatever the people trading perceive it to be. In some cases, that value can be larger than a million dollars (i.e. in countries where their own currency is in a free-fall, where the government is trying to limit the supply of foreign currency, but people want to exchange their local currency for something more stable; people in Argentina, Lebanon, Sri Lanka, and Turkey might want to do that).

If, for whatever reason, Russia pays for North Korean drones to murder Ukrainians, there's absolutely nothing the American government can do about that.