This paper is the second of three articles designed to stabilize the trace formula. The goal is to stabilize the global trace formula for a general connected group, subject to a condition on the fundamental lemma that has been established in some special cases. In the first article [I], we laid out the foundations of the process. We also states a series of local and global theorems, which together amount to a stabilization of each of the terms in the trace formula. In this paper, we shall take a significant step towards the proof of the theorems. We shall reduce the proof of Global Theorem 1 of [I. Sect. 7] to the special case of unipotent elements. This reduction will play a key role in the proof of all of the theorems, which will be carried out in the last of the three articles.
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