Of course, the ability of the ECB to follow an independent European monetary policy will require that the euro float against other major outside currencies, such as the US dollar and the Japanese yen. Thus, in a world of open and integrated financial markets, the exchange rate is a major channel through which monetary policy actions are transmitted to the economy.
Moreover, it is movements in the exchange rate that permit domestic interest rates to diverge from their foreign counterparts for a period of time. For example, an increase in official interest rates by the central bank, in response to demand and inflation pressures in the economy, leads to a stronger currency, which also works to restrain those pressures.