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A homogeneous space G/H is called a reductive symmetric space if G is a (real) reductive Lie group and H is a symmetric subgroup of G, fixed by some involution on G. The representation theory of reductive symmetric spaces was extensively studied in the 1980s and 1990s by Erik van den Ban, Patrick Delorme, Henrik Schlichtkrull, and others, culminating in the Plancherel formula for the L2-space of G/H. This work generalizes the group case established by Harish-Chandra in the early 70s, where G = G' x G' and H is the diagonal subgroup. In our collaborative research with A. Afgoustidis, N. Higson, P. Hochs, and Y. Song, we are exploring this topic from the perspective of C*-algebras and K-theory. I will present these exciting new developments, highlighting novel aspects and differences from the traditional group case.