How to apply a transparent border (I think the technical term is offset) along the perimeter.

Arturo,

As I (mis)understand it, you can use the live Type (not outlined) or outline it, and:

0) Create the background;

1): Type the 4, then:

1A) In the Appearance palette Add New Stroke, give it another colour, and drag it down beneath Characters, set the Stroke Weight so you get the right gap (Stroke Weight = 2 x gap);

1B) Click the stroke in the Appearance palette to select only that, then in the Transparency palette set its Opacity to 0%; now it is invisible, but still there;

2) With the Pen Tool create a rough shape for the (green) element that fits the desired edge to the right (you can outline the 4 to snap to if you wish to have the element flush with the right edge of the 4; the element can extend to cover the part of the 4;

3) Select the 4 from 1) and move it on top of the element, you can hold Ctrl/Cmd and press X and then F, you can see it cover the unwanted parts of the element;

4) Select both the 4 from 1) and the element from 2) and group them; you can hold Ctrl/Cmd and press G;

5) In the Transparency palette options (you may need to click the right arrow to Show options) click the Knockout Group box until the element is knocked out by the transparent stroke of the 4.

This ought to give you the (accurate) desired appearance, and is fully editable/reversible.

Maybe I misunderstand it, but if you want a transparent space between the stroke and the compound path, just add a stroke in the Appearance panel and apply an Offset Path Effect to it.

You might have to expand the Stroke panel to see this but you can position a stroke to be on the outside of a path. You can also use the Offset Path command (there are two) to expand the stroke by half its width.

If you do this in the Effect menu the offset is an editable effect and the path shape does not change, only its appearance does.

If you use Object > Path > Offset Path the path shape will change. This will make a duplicate of the original path.