The methods of Loeffler are promising for every situation,
in which we are given reductive algebraic groups $G\supset H$ over a local field
$F$ with ring of integers $\mathcal O\subset F$ and the smooth functions $\mathcal C^\infty_{c}(H(F)\backslash G(F)/G(\mathcal O))$ form a cyclic module
over the Hecke algebra $\mathcal C^\infty_{c}(G(\mathcal O)\backslash G(F)/G(\mathcal O))$. The work of Soergel centers around studying  Hecke algebras and their categorification in the more general context of
general Coxeter systems$^1$, from which we get the spherical affine Hecke algebra
Loeffler is interested in as an important special case. 
The  applications Soergel is working on mostly concern
representations  of real Lie groups$^2$, rational representations of
algebraic groups and representations of finite groups of Lie type, where
the usual affine Hecke algebra plays a central role$^3$. An
extension of the scope to representations of algebraic groups over
$p$-adic fields together with a link to number theory as provided by Loeffler
would be an excellent fit. 
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1: W. Soergel: Kazhdan-Lusztig-Polynome und unzerlegbare Bimoduln über Polynomringen, Journal of the Inst. of Math. Jussieu (2007) 6(3), 501-525. 
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2: W. Soergel, R. Virk and M. Wendt, Equivariant motives and geometric representation theory, arXiv:1809.05480
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3: W. Soergel,  H.H. Andersen, J.C. Jantzen, Representations of quantum groups at a p'th root of unity and of restricted Lie algebras in characteristic p: Independence of p, Astérisque 220 (1994), 1-320