  A complex manifold $X$ satisfies the Oka-Grauert property if the inclusion
$\Cal O(S,X) \hookrightarrow \Cal C(S,X)$ is a weak equivalence for every Stein
manifold $S$, where the spaces of holomorphic and continuous maps from $S$ to
$X$ are given the compact-open topology. Gromov's Oka principle states that if
$X$ has a spray, then it has the Oka-Grauert property. The purpose of this
paper is to investigate the Oka-Grauert property using homotopical algebra. We
embed the category of complex manifolds into the model category of simplicial
sheaves on the site of Stein manifolds. Our main result is that the Oka-Grauert
property is equivalent to $X$ representing a finite homotopy sheaf on the Stein
site. This expresses the Oka-Grauert property in purely holomorphic terms,
without reference to continuous maps.
