What is the meaning of しちまおう?


I'm playing a video game and in this scene the character is on a hill and
says:

> このまま昼寝しちまおうか

My guess is that it's a conjugation of する but it doesn't look close to する at
all.

What conjugations are present in that word and how does it affect the
sentence's overall meaning?




Like snailplane commented, it is a contracted form of して しまう.  
I would add that the final ～おう marks the volitional form of しまう. If that can
help you understand better the sentence, an other very similar way of saying
it would be:

> このまま昼ねを して しまいましょう か




Like snailplane commented, it is a contracted form of して しまう.  
I would add that the final ～おう marks the volitional form of しまう. If that can
help you understand better the sentence, an other very similar way of saying
it would be:

> このまま昼ねを して しまいましょう か

