Can you omit the 的 after 举办 in 北京奥运会是2008年举办的？
北京奥运会是2008年举办的。

&quot;北京奥运会是2008年举办的&quot; is a [topic + comment/opinion] sentence

Topic: 北京奥运会 (Beijing Olympics)

Comment: 是 2008年 举办的 (is hosted by 2008)


(It is obviously wrong, it makes 2008年 the subject. I will state the correct sentence later in this post)
The '的' here is a [possessive marker]. It marks the omitted object to be possessed by [2008年]

2008年 举办的(项目)
2008年 is the subject; 项目 (or other noun refers to 北京奥运会) is the omitted object

The correct sentence should be:

&quot;北京奥运会是在 2008年 举办的&quot; (Beijing Olympics is hosted in 2008)
the subject '北京' is omitted, &quot;北京奥运会是(北京)在 2008年 举办的&quot;

In this sentence,  '的' is an [adjective marker]. It turns &quot;在 2008年举办&quot; into an adjective phrase &quot;在 2008年 举办的&quot;
This adjective phrase describes 北京奥运会 (Beijing Olympics that is hosted in 2008)
'的' cannot be omitted in this sentence.
To avoid using 的, you can change this [topic + comment/opinion] sentence into a [SVO] sentence and write &quot;(北京)在 2008年 举办北京奥运会&quot; - &quot;(Beijing) held the Beijing Olympic Games in 2008&quot;
Since we do not omit the subject '北京' here, we can omit the '北京' in '北京奥运会' instead -- &quot;北京在 2008年 举办(北京)奥运会&quot;