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Ok, I'll admit, this is a really weird question.

What I'm trying to do is have a transparent stroke. By that, I mean that the stroke takes up space, but it's showing what's behind the object.

When I set the stroke alpha down to 0, it turns the same color as the fill, which isn't what I want.

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Haha, I love it when I solve a problem three minutes after asking online. ;)

I just had to scale-resize the object to it's size minus half the stroke and remove the stroke. e.g. with an object 80 pixels high and 40 pixels wide, with a 4 pixel stroke, go to Object -> Transform, and use 78 for the height (80 - 4/2 = 78) and 38 for the width (40 - 4/2 = 38). Then you just remove the stroke.

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    Its perfectly normal that taking the time to explain yourself to others explains the problem to yourself with sufficient clarity so that you can solve it yourself. – joojaa Apr 19 '17 at 6:49
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An obvious solution is to have two copies - one with only the fill and one with only the stroke. Resizing the fill to smaller should do the job. But proportional shrinking gives perfect result only in rare cases. The result can be accurate enough if the shape is convex and the stroke is narrow. Non-convex shape with a heavy stroke needs more complex tinkering. See the following cartoon:

enter image description here

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