A transport problem for the particle density function $n(x,v,t)$ in the bounded region $[-b,+b]$ is considered. The particle velocities are assumed to be unbounded. The boundary conditions are expressed by means of a general {\em multiplying} boundary operator $\Lambda$, relating the incoming and outgoing flux of particles. The generation of a B-bounded semigroup (see [1], [2], [3]) is proved, and the solution of the transport problem is explicitly given by means of the B-bounded semigroup.