[Framers] CMYK color matching from InDesign to Frame

[Doug]

I've been tasked to develop a template in Frame that uses the same CMYK
color set as a document someone else created in InDesign.  I'm seeing a big
problem here.

When I define a color in Frame by entering the CMYK code, the color that
displays on-screen isn't the same as the color in InDesign, even though the
CMYK code is identical.

However, if I enter the RGB equivalent code in Frame, the color displays
accurately on-screen (on some colors--others are still off).

In short, RGB codes in InDesign usually display the same shade in Frame,
but CMYK codes never display in Frame the same as they display in InDesign.

Can someone explain why this is happening, and what I can do to resolve it?

Thanks,

Doug