An alternative approach to the classical Morel–Voevodsky stable motivic homotopy theory
S
H
(
k
)
SH(k)
is suggested. The triangulated category of framed bispectra
S
H
nis
fr
(
k
)
SH_{\operatorname {nis}}^{\operatorname {fr}}(k)
and effective framed bispectra
S
H
nis
fr
,
eff
(
k
)
SH_{\operatorname {nis}}^{\operatorname {fr},\operatorname {eff}}(k)
are introduced in the paper. Both triangulated categories only involve Nisnevich local equivalences and have nothing to do with any kind of motivic equivalences. It is shown that
S
H
nis
fr
(
k
)
SH_{\operatorname {nis}}^{\operatorname {fr}}(k)
and
S
H
nis
fr
,
eff
(
k
)
SH_{\operatorname {nis}}^{\operatorname {fr},\operatorname {eff}}(k)
recover classical Morel–Voevodsky triangulated categories of bispectra
S
H
(
k
)
SH(k)
and effective bispectra
S
H
eff
(
k
)
SH^{\operatorname {eff}}(k)
respectively.
Also,
S
H
(
k
)
SH(k)
and
S
H
eff
(
k
)
SH^{\operatorname {eff}}(k)
are recovered as the triangulated category of framed motivic spectral functors
S
H
S
1
fr
[
F
r
0
(
k
)
]
SH_{S^1}^{\operatorname {fr}}[\mathcal {F}r_0(k)]
and the triangulated category of framed motives
S
H
fr
(
k
)
\mathcal {SH}^{\operatorname {fr}}(k)
constructed in the paper.