L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld : Decomposition cellulaire de la tour de Lubin-Tate

This article is the first one of a series aiming to construct an isomorphism between the p-adic Lubin-Tate and Drinfeld towers, describe this isomorphism and give applications. We construct a p-adic equivariant integral model of the Lubin-Tate tower with infinite level. This formal scheme will be later compared to another one associated to the Drinfeld tower.