Ambiguous divisor classes in function fields

Let $\text{L}\text{K}$ be a Galois extension of algegraic function fields in one variable with Galois group G. Let J_K and J_L be the divisor classes of degree zero in K and L, respectively. A study is made of the kernel and cokernel of the natural map from J_K to $\text{J}{}_{\mathrm{L}}{}^{\mathrm{G}}$.