Question about Bloch function in Reduced Zone Scheme

ck00

The classical textbook, Introduction to solid state physics by Charles Kittle said:
"If we encounter a Bloch function written as [tex]ψ_{k’}(r)=exp(i{k’}r) u_{k’}(r)[/tex], with k’ outside the first zone, we may find a suitable reciprocal lattice vector G such that k=k’+G lies within the first Brillouin zone. Then
[tex]ψ_{k’}(r)=exp(ik’r) u_{k’}(r)=exp(ikr) [exp(-iGr) u_{k’}(r)][/tex]
[tex]=exp(ikr) u_k(r)=ψ_k(r)[/tex]"
I wonder why [tex]exp(-iGr) u_{k’}(r)=u_k(r)[/tex], how to derive this relation?

0xDEADBEEF

He probably defines [itex]u_k(r)[/itex] this way. It is just the old u times a complex phase.