Let G be a k-analytic group, and let H be a closed subgroup of G. Then does there exist a k-analytic space, which can be reasonably called the quotient G/H?

Commentary: I realise that I am not being overly precise here. This is partly because I am not sure in exactly what form I want to ask this question. In lieu of this, I will mention an example, that I suspect may produce an interesting quotient space.

Let Spec(A) be an affine group scheme of finite type over k^{o}. Let G be the analytification of the generic fibre of Spec(A). On $A\otimes_{k^\circ} k$, one can define the seminorm where ||a|| is defined to be the infimum of all |t| where $t\in k^\times$ is such that $a\in tA=t(A\otimes_{k^\circ} 1)\subset A\otimes_{k^\circ} k$. Take the completion of this tensor product with respect to this seminorm, and let H be its spectrum (which is then naturally an affinoid subgroup of G).