I have a problem when copying an image from Adobe Illustrator CC 2014 to Pages. The color of the image changes when pasted into Pages (5.5.3, OSX Yosemite 10.10.5). Pages actually changes the picture's RGB/CMYK/HSB values. I've tried switching between CMYK/RGB color modes in Illustrator, but the problem occurred with both settings. I haven't found any relevant color settings in Pages. Have you got any ideas how to fix this issue?
You should EXPORT your images from Illustrator (Menu "file" then "Export") instead of copy/pasting directly from one software to the other.
I made some tests and the worst result was happening when doing that copy/paste; the colors are very different from the original file.
So export your image into a JPG or PNG format, and then INSERT it in Pages using the "insert" menu and choosing your file from there. The colors are still not 100% the same but the variations are barely visible this way.
Using color profile or not doesn't change anything with Pages, I don't think it recognize any color management data and it doesn't have any option either to turn this on/off.
Working in RGB is probably the best for Pages if you need to use your document for web or for a presentation. But for printing you should still use CMYK; CMYK will look a bit different from the original in Pages.
As I said in my comment, Pages isn't a software where you can have much control on colors and I guess inserting your images this way instead of copy/pasting them is the best you can do. If you want precision then you'll need to use another software, like the ones offered by Adobe.
If you want a real solution use InDesign. If you want to stick to pages though, see if the problem still exists after exporting the pages file to whatever format you'll need. If yes you'll have to either export your images from illustrator and then import again into pages or change your color settings in illustrator(there are different color spaces for RGB/CMYK) if you find one that matches pages let us know.