是......的, it is a sentence drill very useful which indicates emphasis. As a structure, they need one and another. As for your omission, we do it on 是,instead of 的。Here we can try to from your sentence: 北京奥运会是2008年举办的,
1, 北京奥运会2008年举办的。
2,To compare this, 2008年奥运会【是北京举办的】,the place 北京 is emphasized. You can say also:
2008年奥运会北京举办的。