  The homotopy fiber of the inclusion from the long embedding space to the long
immersion space is known to be an iterated based loop space (if the codimension
is greater than two). In this paper we deloop the homotopy fiber to obtain the
topological Stiefel manifold, combining results of Lashof and of Lees. We also
give a delooping of the long embedding space, which can be regarded as a
version of Morlet-Burghelea-Lashof's delooping of the diffeomorphism group of
the disk relative to the boundary. As a corollary, we show that the homotopy
fiber is weakly equivalent to a space on which the framed little disks operad
acts possibly nontrivially, and hence its rational homology is a (higher)
BV-algebra in a stable range of dimensions.
