Reference for Manin's idea on algebraic geometry over the symmetric monoidal model category of Motives

The only reference ever given for this is

Y. Manin, Letter, March 2000

I don't think this letter (from Manin to Bertrand Toen, I presume) has ever been made public, and definitely it hasn't been published. But you might want to try asking Toen for a copy.

As you known, some of the math involved was worked out in Spitzweck's thesis, "Operads, Algebras and Modules in Model Categories and Motives". Note that he thanks Toen in the introduction, and Manin is listed as "Korreferent".

Not really an answer, but as a complement to Myshkin's, let me just mention a predecessor : Deligne's very famous (and magnificent) article

Deligne, P. Le groupe fondamental de la droite projective moins trois points.

available here

especially the two paragraphs

§5 Géométrie algébrique dans une catégorie tannakienne

§7 Géométrie algébrique dans la catégorie tannakienne des systèmes de réalisations: interprétations