With representation-theoretic applications in mind, we construct a formalism of reduced
motives with integral coefficients. These are motivic sheaves from which the higher motivic …

We show that representations of convolution algebras such as Lustzig's graded affine Hecke
algebra or the quiver Hecke algebra and quiver Schur algebra in type A and A˜ can be …

We provide a uniform construction of" mixed versions" or" graded lifts" in the sense of
Beilinson-Ginzburg-Soergel which works for arbitrary Artin stacks. In particular, we obtain a …

For a large class of good moduli spaces $ X $ of symmetric stacks $\mathcal {X} $, we define
noncommutative motives $\mathbb {D}^{\text {nc}}(X) $ which can be regarded as …

We construct a geometric realization of categories of representations of affine Hecke
algebras and split reductive $ p $-adic groups via a $ K $-motivic Springer theory. We …

We prove that the derived direct image of the constant sheaf with field coefficients under any
proper map with smooth source contains a canonical summand. This summand, which we …

We initiate the study of KK‐theory Soergel bimodules, a global and KK‐theoretic version of
Soergel bimodules. We show that morphisms of KK‐theory Soergel bimodules can be …

For a proper map $ f: X\to S $ between varieties over $\mathbb {C} $ with $ X $ smooth, we
introduce increasing filtrations $\textbf {P}^{\leq\cdot} _f\subset P^{\leq\cdot} _f $ on $\text …