  We study the production of cosmic rays (CRs) in supernova remnants (SNRs),
including the reacceleration of background galactic cosmic rays (GCRs) - thus
refining the early considerations by Blandford & Ostriker (1980) and Wandel et
al. (1987) - and the effects of the nuclear spallation inside the sources (the
SNRs). This combines for the first time nuclear spallation inside CR sources
and in the diffuse interstellar medium, as well as reacceleration, with the
injection and subsequent acceleration of suprathermal particles from the
postshock thermal pool. Selfconsistent CR spectra are calculated on the basis
of the nonlinear kinetic model. It is shown that GCR reacceleration and CR
spallation produce a measurable effect at high energies, especially in the
secondary to primary (s/p) ratio, making its energy-dependence substantially
flatter than predicted by the standard model. Quantitatively, the effect
depends strongly upon the density of the surrounding circumstellar matter. GCR
reacceleration dominates secondary CR production for a low circumstellar
density. It increases the expected s/p ratio substantially and flattens its
spectrum to an almost energy-independent form for energies larger than 100
GeV/n if the supernovae explode on average into a hot dilute medium with
hydrogen number density $N_H=0.003$cm$^{-3}$. The contribution of CR spallation
inside SNRs to the s/p ratio increases with increasing circumstellar density
and becomes dominant for $N_H\gsim 1$ cm$^{-3}$, leading at high energies to a
flat s/p ratio which is only by a factor of three lower than in the case of the
hot medium. Measurements of the boron to carbon ratio at energies above 100
GeV/n could be used in comparison with the values predicted here as a
consistency test for the supernova origin of the GCRs.
