OK, I could find a workaround. Instead of applying the Object Style, I manually applied all the attributed to the object, by way of the Anchored Object dialog box.
So, the problem seems directly related to the Style.
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Are you talking about the red lines? Are they visible when the group is pasted inline BEFORE applying the object style?
What version of ID? Is it patched to the latest release? OS?
Yes, I'm talking about the red lines. They are still visible when I past the group inline, but I don't apply the object style. ID is version 7.0.4, and all patches have been applied. I'm on a Mac with OS X 10.6.8.
SOLVED: The object style also included strike attributes, that where permanently changed when applying the style. I don't know when I activated them, but they where there and editing the style just had it working back as I wanted.