Looking for a movie in which girl escorted to safety

Hi, looking for a movie in which I only remember a few things. The main plot was that a young teenage girl had to be transported to safety by a tough guy ( the main role). I remember that there was a submarine that emerged through the ice and there was a brutal cage fighting in a box, one of the fighters was trying to protect the girl but the main guy thought this was a threat and killed him in the box and the girl cried over the misunderstanding. I think she was safely handed over to her father at the end

Sounds like Babylon A.D. with Vin Diesel: Babylon A.D. (2008) - IMDb

Trailer has the cage fight and submarine: Babylon A.D. (2008) - English trailer - YouTube

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