SGA 3, expose 12, remark 1.6 says that one can easily construct a group scheme over a discrete valuation ring with generic fiber Gm and special fiber Ga. 


What is such an example?



Constructing a degeneration (as a group scheme) of G_m to G_a
R[x,y]/(y^2-x^3-\pi x^2) gives the coordinate ring of a bad cubic curve, where \pi is a uniformizer in R. Remove the origin (which is the one singular point), and projectivize the curve by adding a point at infinity, so your group has an identity.


The generic fiber (treating \pi as a unit) is then the smooth part of a nodal cubic, yielding **G**m, and the special fiber (setting \pi to zero) is the smooth part of a cuspdal cubic, yielding **G**a.


