Where is a soccer stadium in which the teams not only switch sides at half time, but also switch hemispheres?

Yes, it exists! The "Zerão", or Big Zero Soccer Stadium in Macapá, the capital city of the State of Amapá in Northeastern Brazil, was built in such a position that the Equator precisely overlaps the field's centerline.

This means that at half time, when the two teams switch sides on the field, they also move from one half of the world to the other! The team that defends the goal in the Northern Hemisphere in the first half of the match will play the second half defending the goal in the Southern Hemisphere, and obviously they will be running from one half of Earth to the other and back for 90 minutes or more!

The Equator crosses the city of Macapá, where an avenue has half of its buildings on the Southern Hemisphere and the other half in the Northern half of the world, and the neighborhoods are - literally - on the North or South sides of town...