Are quantum effects also affected by special relativity? Imagine I've two boxes with 100 radioactive (eg alpha) decay particles with a half life of 10 years. One box stays on Earth and the other is travelling close to speed of light and this box returns to Earth after 10 years. Are the number of decayed particles the same?
 A: You ask in the title:

Are quantum effects also affected by special relativity?

Yes they are.  
In the example you propose, 

Are the number of decayed particles the same?

the answer is "no they are not". As an example, I recommend you study this experiment:
https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment 
A: That actually works with muons produced in the upper atmosphere.
Because of their 2 µs lifetime, very few of them would reach the ground, if they were not traveling at relativistic speeds. In fact, most of them do reach the ground because of the relativistic time dilation.
A: Yes, particle decay is affected by time dilation. You can see this effect in high energy experiments, where the expected decay length of an unstable particle is given by $$l=\gamma v\tau\approx \gamma c\tau $$
That is, higher energy particles take longer to decay because of time dilation. Muons have a lifetime of $2.2\rm\mu s $, but because of this effect, the average muon lifetime in the g-2 experiment at Brookhaven was significantly longer. Similar effects are seen in all high energy physics experiments.
