  We formulate and prove a Conner-Floyd isomorphism for the algebraic K-theory
of arbitrary qcqs derived schemes. To that end, we study a stable
$\infty$-category of non-$\mathbb A^1$-invariant motivic spectra, which turns
out to be equivalent to the $\infty$-category of fundamental motivic spectra
satisfying elementary blowup excision, previously introduced by the first and
third authors. We prove that this $\infty$-category satisfies $\mathbb
P^1$-homotopy invariance and weighted $\mathbb A^1$-homotopy invariance, which
we use in place of $\mathbb A^1$-homotopy invariance to obtain analogues of
several key results from $\mathbb A^1$-homotopy theory. These allow us in
particular to define a universal oriented motivic $\mathbb E_\infty$-ring
spectrum $\mathrm{MGL}$. We then prove that the algebraic K-theory of a qcqs
derived scheme $X$ can be recovered from its $\mathrm{MGL}$-cohomology via a
Conner-Floyd isomorphism \[\mathrm{MGL}^{**}(X)\otimes_{\mathrm L}\mathbb
Z[\beta^{\pm 1}]\simeq \mathrm K^{**}(X),\] where $\mathrm L$ is the Lazard
ring and $\mathrm K^{p,q}(X)=\mathrm K_{2q-p}(X)$. Finally, we prove a Snaith
theorem for the periodized version of $\mathrm{MGL}$.
