Hi Alan and welcome.
CTA does not allow you to save a character with animations from a project time line as it were.
You can save the characters animations, either as one or many different ones as motion clips.
Then you can add that motion clip to the characters action menu to apply as needed.
The action menu items are saved with the character so you can copy the character to other projects and reference the same Actions for that character.
Keep in mind that the Action items point to clips that, I believe, are saved separately from the character in the custom folder.
For defining and creating clips and actions see the Help under:
Animations | Character Animations - Body Animations | Utilizing the Action Menu for Motions
Hope that helps.
Jeff
Get my Plugin Manager and TaskNotes plugins for iClone.
Check out EZColors and Other products for CTA/CA. EZColors: the easy way to change Render Styled (RS) colors!
See my CTA Tutorials on the YouTube channel CTAStepByStep