Let
B
G
BG
be the classifying space of a compact Lie group
G
G
. Some examples of computations of the motivic cohomology
H
∗
,
∗
(
B
G
;
Z
/
p
)
H^{*,*}(BG;\mathbb {Z}/p)
are given, by comparing with
H
∗
(
B
G
;
Z
/
p
)
H^*(BG;\mathbb {Z}/p)
,
C
H
∗
(
B
G
)
CH^*(BG)
and
B
P
∗
(
B
G
)
BP^*(BG)
.