Not just UV but also ozone, evaporation of the oils in the rubber, heat and cold.

This is what decays tires:
Storing them on a cold floor or cold in general
Storing them next to an electric motor
Storing them in the sun
Storing them in a hot garage

The expanding and contracting of the rubber will literally squeeze the oils out of the tire making it hard and not pliable - which is what makes the tire hold the road and stick.

Best ways to store a tire:
In a plastic bag. Seals the tire so it doesn't evaporate as much.
In a controlled environment like a finished basement (I used to stack my tires in my apartment with a board and table cloth over them and used as a table)
With the air pressure around 25psi
Not stacked on top of each other