The Jacquet-Langlands correspondence tells us how to transfer automorphic representations between inner forms of a general linear group over a global field. I will explain how this should generalize in light of the conjectural description of the automorphic spectrum in terms of Langlands/Arthur parameters. Applying this idea I will try to answer the following question when $G_1$ and $G_2$ are unitary groups. Question: Let $G_1$ and $G_2$ be reductive groups over a number field which are inner forms of each other such that their adelic groups are isomorphic as topological groups. When are their automorphic spectra isomorphic as modules over the adelic group?
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