In classical topology, different cobordism theories can be thought of as uni- versal cohomology theories with certain orientations. For example, complex cobordism MU is the universal complex oriented cohomology theory; that is cohomology theories with Thom isomorphism for every complex vector bundle. The analogous idea of different notions of orientations, and corresponding alge- braic cobordism theories are well studied in $\mathbb{A}^1$-homotopy theory. I will mostly talk about special linear, and “metalinear” orientations, and their corresponding universal algebraic theories in the context of $\mathbb{A}^1$-homotopy theory. I would like to report on some ongoing computations of stable homotopy groups of special and metalinear algebraic cobordism. This is joint work in progress with Egor Zolotarev.