  The influence of the metallicity at the main sequence on the chemical
structure of the exploding white dwarf, the nucleosynthesis during the
explosion and the light curves of an individual Type Ia supernovae have been
studied. Detailed calculations of the stellar evolution, the explosion, and
light curves of delayed detonation models are presented.
  Detailed stellar evolution calculations with a main sequence mass of 7 M_o
have been performed to test the influence of the metallicity Z on the structure
of the progenitor. A change of Z influences the central helium burning and,
consequently, the size of the C/O core which becomes a C/O white dwarf and its
C/O ratio. Subsequently, the white dwarf may grow to the Chandrasekhar mass and
explode as a Type Ia supernovae. Consequently, the C/O structure of the
exploding white dwarf depends on Z. Since C and O are the fuel for the
thermonuclear explosion, Z indirectly changes the energetics of the explosion.
  In our example, changing Z from Pop I to Pop II causes a change in the zero
point of the maximum brightness/decline relation by about $0.1^m$ and a change
in the rise time by about 1 day. Combined with previous studies, We provide a
relation between a change of the rise time in SNeIa and the off-set in the
brightness/decline relation. We find that dM = dt where dM is the offset in the
relation and dt is the change of the rise time in days.
  This relation provides a way to detect and test for evolutionary effects, and
to estimate the possible consequences for the determination of the cosmological
constant. However, due to uncertainties in the time evolution of the properties
of the progenitors, we cannot predict whether evolution becomes important at
z=0.5, 1 or 2. This question has to be answered by observations.
