The Tuxedo (2002)
introduction as "The Last Emperor of Soul"
a poster for the movie is seen
title seen at video store
Cortex did some Jackie Chan's stunts from this movie
A DVD vendor recommends the film to his customers
poster in projectionist's room
When Rachel is browsing through the videos at the fair, The Tuxedo is one of them
Mentioned in the question
opening shows footage from this other Jackie Chan movie.