Dating a girl who already has a boyfriend?

So here it goes-In my cl there's this girl, whom a have a huge crush for- she's gorgeous, stylish and intellectual, smiley but a bit icy. I've been subtly trying to let her know that I really like her- a smile, a conversation, debates and stuff BUT, at some point I heard her saying that she has a boyfriend in her home country, the Czech republic. She's been giving me mixed signals- at times she's kinna cold at other times she smiles and tries to tell me jokes and ask me stuff about myself. How should I deal with this? I'm a confident guy, with common-sense, well-read and respectful, in control of my feelings and emotions, not dominant but relaxed in a way that females find attractive- but this time it's the other way around- this girl has really managed to mess my mind up :). Should I ask her out? How do should I proceed?