Swiss International Airlines - Ticket via callcenter billed in wrong currency

I was wondering, is it normal for SWISS air to bill my credit card in a different currency than the one stated everywhere? Webpage, call centre when booking, my electronic receipt/ticket all state a price in Danish Kronor, flight out of CPH, so this is exactly what it should be and what I agreed on. The charge however is in USD, at an exchange rate which is great for them but not for me. Is that a normal procedure? I don't feel like making a fuzz about nothing, but this seems very odd to me and I feel a bit cheated by them. But then again the difference in the end is probably not big enough to spend too much time following it up. Any advice/opinion?

Follow it up..... it's a pretty common "scam". Probably executed by the payment provider / bank of Swiss where the transaction is handled.

They are supposed to offer you the choice, but rarely do. And the exchange rate used is always bad for you.

You never asked to be billed in USD, so you should call them and ask them to cancel the payment and charge you again (in DKK). Even if the difference is small, they have to learn not to do this.