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I have to admit I don't know much about topics appearing in this question, I just see very rough connections between these objects:

According to this page 23, a different $t$-structure on $D^b(\text{Coh}_X)$ is considered that its heart produces the same algebraic $K$-groups ($G$-groups). The definition of the $t$-structure is the reminiscent of the classical perverse sheaves, defined using a perversity function. The difference that I see that perverse sheaves are usually defined in the category of sheaves of abelian groups rather than $\mathcal{O}_X$-modules. There is also Riemann-Hilbert correspondence between perverse sheaves and $D$-modules. I was wondering whether it is possible to recover higher algebraic $K$-groups of regular varieties by taking the $K$-theory of some specific type of $D$-modules?

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    $\begingroup$ The distinction between coherent and constructible sheaves here is pretty important. That seems like a pretty big issue for any approach along these lines.. $\endgroup$
    – Ben Webster ♦
    Commented Feb 20, 2021 at 21:19
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    $\begingroup$ The $K$-theory of constructible sheaves (or, equivalently, of regular holonomic $D$-modules) just gives constructible functions with values in the $K$-theory of the ring of coefficients. See Lemma 3.3 of this paper of Beilinson: arXiv:math/0610055 $\endgroup$
    – D.-C. Cisinski
    Commented Feb 20, 2021 at 22:14

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