  In this paper, we study the algebraic cobordism spectrum $MSL$ in the motivic
stable homotopy category of Voevodsky over an arbitrary perfect field $k$.
Using the motivic Adams spectral sequence, we compute the geometric part of the
$\eta$-completion of $MSL$ (modulo the maximal subgroup that is $l$-divisble
for all primes $l\neq2, char k$). As an application, we study the Krichever's
elliptic genus with integral coefficients, restricted to $MSL$. We determine
its image, and identify its kernel as the ideal generated by differences of
$SL$-flops. This was proved by B. Totaro in the complex analytic setting. In
the appendix, we prove some convergence properties of the motivic Adams
spectral sequence.
