What book by Bosch? Anyway, maybe the answer is here: mathoverflow.net/questions/51095/…

See arxiv.org/pdf/1308.3187v1.pdf

One example of a complex oriented cohomology theory that is not Landweber exact is $H\mathbb{Z}$.

@FernandoMuro For $Y,\{X_i\} \in \text{Loc}(b)$ we have $[Y,W \prod_i {X_i}] = [i(Y),\prod {X_i}] = \prod_i [i(Y),X_i] = \prod_i [Y,W(X_i)]$. So I think the product is just the product in $D(A)$ followed by $W$.

Is there any reason to suspect this is true? Take $A = D(R)$ for, say, a Noetherian regular local ring $(R,\mathfrak{m},k)$, and take $b = k$. The localizing subcategory generated by $k$ is then the derived category $\mathfrak{m}$-torsion $R$-modules. The inclusion will not, in general, preserve limits.

OK, the latter is the same as arxiv.org/pdf/1811.05729.pdf, and is also coauthored by Isaksen.

$\pi_{1,0}\mathbb{1}$ (I always get confused by motivic grading) is computed in arxiv.org/pdf/1604.00365.pdf. For an expository article, perhaps: Østvær, Paul Arne (2020). Motivic stable homotopy groups, In Haynes Miller (ed.), Handbook of Homotopy Theory. Chapman & Hall/CRC. ISBN 9780815369707. Motivic stable homotopy groups. s 759 - 793

It's also true for G=F_4, see arxiv.org/pdf/0903.4865.pdf

In addition, the appendix to "On topological cyclic homology", in particular Theorem A.7 has the statement you want as well.

Ragnarsson's paper links to 'Classifying G-spaces and the Segal conjecture' - did you check there?

It holds, for example, if A is a projective Z[G]-module (III.1.1(c) in Brown's book 'Cohomology of Groups')

@MarcHoyois Is it true that Cisinski proves this for a general qcqs scheme? My French isn't very good, but it seems like it is shown for Noetherian schemes of finite Krull dimension ('ans ce qui suit, tous les schémas seront noethériens, de dimension de Krull finie.')

Dear Badam, I'm not sure, but it seems to be difficult/unknown. There is a paper of Auslander which considers the case of global dimension of algebras over a field, but this is as much as a I could find.