Let be a tamely ramified connected reductive group defined over a non-archimedean local field k. We show that the Bernstein center of a tame supercuspidal block of is isomorphic to the Bernstein center of a depth-zero supercuspidal block of for some twisted Levi subgroup of of .
The author is very thankful to Rainer Weissauer, Jeff Adler, Sandeep Varma and David Kazhdan for many helpful interactions. He is especially grateful to Jiu-Kang Yu for his careful proof reading and making important suggestions. He is also thankful to the Math Institute at Heidelberg University for supporting his stay during which this work was written.
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