  We reprove the Lefschetz trace formula for Lubin-Tate spaces, based on the
locally finite cell decompositions of these spaces obtained by Fargues, and
Mieda's theorem of Lefschetz trace formula for certain open adic spaces
(\cite{Mi1} theorem 3.13). This proof is rather different from those of Strauch
in \cite{St} (theorem 3.3.1) and of Mieda in \cite{Mi1} (example 4.21), and is
quite hopeful to generalized to some other Rapoport-Zink spaces as soon as
there exist suitable cell decompositions. For example, we proved a Lefschetz
trace formula for some unitary Rapoport-Zink spaces in \cite{Sh} by using
similar ideas here.
