A primer for unstable motivic homotopy theory (Antieau and Elmanto)
An introductory course on motivic homotopy theory and rational mixed motives (Déglise)
Comparison of cobordism theories (Levine)
Motivic Homotopy Theory (2002 Norway lectures (Springer))
Robalo:
Noncommutative Motives I: A Universal Characterization of the Motivic Stable Homotopy Theory of Schemes, 2013
, or
K-theory and the bridge from motives to noncommutative motives
(among other things, establishes the abstract foundations for unstable and stable motivic categories)
Ayoub: The motivic Thom spectrum and the algebraic cobordism (also mentions Thom isomorphism)
Panin: Oriented cohomology theories of algebraic varieties (2003)
A universality theorem for Voevodsky's algebraic cobordism spectrum (metions Thom isomorphism in 2.0.4?)
Motivic homotopy theory in derived algebraic geometry
(Adeel Khan's thesis)
Motivic spectra and universality of K-theory
Notes on motivic infinite loop space theory
Motivic model categories and motivic derived algebraic geometry
("motivic" versions of ∞-categories, ∞-topoi, spectral schemes and spectral Deligne--Mumford stacks; vector bundles, Thom spaces, cobordism for motivic stacks)
Modules over motivic ring spectra
Motivic infinite loop spaces
Modules over algebraic cobordism
The localization theorem for framed motivic spaces
(framed motivic spectra are equivalent to motivic spectra over arbitrary schemes)
Framed transfers and motivic fundamental classes
On the infinite loop spaces of algebraic cobordism and the motivic sphere
Motivic colimits and extended powers
(colimits for diagrams in a motivic category indexed by a presheaf of spaces)
Milnor excision for motivic spectra
Algebraic cobordism and étale cohomology
Algebraic K-theory of quasi-smooth blow-ups and cdh descent
Cdh descent in equivariant homotopy K-theory
(also contains results on motivic localization of BG)