Half-unknotted 2-orbifolds in orientable spherical 3-orbifolds

If an embedding of a 2-orbifold in an orientable spherical 3-orbifold splits the 3-orbifold into two parts such that at least one part is a handlebody orbifold, then we call it half-unknotted. We will give dierent kinds of algebraic conditions on the embedding such that it is half-unknotted. The results will be applied to questions about extendable actions on surfaces. As an example, we will show that embeddings realizing the maximum order of extendable cyclic actions on genus g > 1 surfaces must be unknotted.