This is a jigsaw killer. Each row, column and jigsaw group contains 1-8 and two *s, which count as zero. Stars cannot touch horizontally, vertically or diagonally.
Since there are 10 rows and columns, I’ve labelled them 1-9 and A; CA is the right-hand column, RA is the bottom row. Jigsaw groups are identified by their upper-left cells, for example JR1C5.
On my earlier attempts, after doing the 3(4) cage I’d forgotten about stars not touching so I started again and have made a point of emphasising this feature.
Prelims
a) 7(3) cage at R1C2, no 8
b) 8(4) cage at R1C2, no 8
c) 8(2) cage at R1CA, no 4, can only have one *
d) 9(2) cage at R2C7, no *
e) 2(2) cage at R3C3 = {2*}
f) 10(2) cage at R3C4, no 1,5,*
g) 10(2) cage at R4CA, no 1,5,*
h) 7(2) cage at R5C2, no 8, can only have one *
i) 6(2) cage at R5C4, no 7,8, can only have one *
j) 3(4) cage at R5C9 = {12**}
k) 7(2) cage at R6C1, no 8, can only have one *
l) 14(2) cage at R6C2 = {68}
m) 7(2) cage at R6C4, no 8, can only have one *
n) 14(2) cage at R9C1 = {68}
o) 3(3) cage at R9C7, no 4,5,6,7,8
p) 3(3) cage at RAC4, no 4,5,6,7,8
1a. Naked pair {2*} in 2(2) cage at R3C3, 2 and one * locked for C3 and JR2C2; at this stage 7(2) cage at R5C2 retains one *
1b. Naked pair {68} in 14(2) cage at R6C2, locked for R6
1c. Naked pair {68} in 14(2) cage at R9C1, locked for R9 and JR6C1
1d. Naked pair {68} in R69C2, locked for C2
1e. Naked pair {68} in 14(2) cage at R6C2, CPE no 6,8 in R25C3
1f. 10(2) cage at R3C4 = {37/46}, no 8
1g. 7(2) cage at R5C2 = {7*} (cannot be {34} which clashes with 10(2) cage), 7 and one * locked for R5 and JR2C2, clean-up: no 3 in R4CA
1h. 10(2) cage = {46}, locked for R3 and JR2C2 -> R6C2 = 8, R6C3 = 6, 14(2) cage at R9C1 = [86], clean-up: no 3,5 in R2C7
1i. 7(2) cage at R6C1 = {25/34/7*}, no 1
1j. 7(2) cage at R6C4 = {25/34/7*}, no 1
1k. R2C23 = {135} (no stars) -> 9(3) cage at R2C1 = {135}, locked for R2, clean-up: no 3,5,7 in R1CA, no 8 in R3C7
[I tend to only use Law of Leftovers (LoL) for harder jigsaws and jigsaw killers. However since HATMAN posted a comment about using LoL, it could be used after step 1 for C123, R12C4 + 10(2) cage at R3C4 must exactly equal R678C3 + R8C2, 10(2) cage = {46} -> no 4,6 in R12C4, R78C3 + R8C2 must contain 4, locked for JR6C3.]
2. 3(4) cage at R5C9 = {12**}, * cannot be touching even diagonally -> R5C9 = *, R6C7 = *, R6C89 = {12}, locked for R6 and JR5C9, no *s in cells touching R5C9 and R6C7, clean-up: no 5 in R7C1, no 5 in R7C4
2a. 7(2) cage at R5C2 = {7*}, R5C9 = * -> no other * in R5
2b. 11(3) cage at R7C7 = {38*/47*/56*) -> R7C78 = {38/47/56}, R7C9 = *
2c. R57C9 = {**}, locked for C9 and JR5C9
2d. 6(2) cage at R5C4 = {15/24}, no 3,6
3. 36 rule on JR1C7 + JR2C7, 1 innie R6C7 = * -> 2 outies R45C6 = 15 = [78], clean-up: no 2 in R4CA, no 3 in R5CA
[or as HATMAN pointed out R5C6 = R6C2 from LoL R12345]
3a. R45C6 = 15 -> R45C7 = 6 = {15/24}/[*6], no 3, no 6 in R4C7
3b. 8(2) cage at R1CA = [17/8*/*8] (cannot be {26} which clashes with 10(2) cage at R4CA), no 2,6
3c. 36 rule on JR5C9 1 innie R8C8 = 1 outie R9CA + 7 -> R8C8 = {78}, R9CA = {1*}
3d. 3(3) cage at R9C7 + R9CA = 3(4)/4(4) = {12**/13**}, no other 1 or * in R9 and JR8C7
3e. 36 rule on CA 2 innies R30CA = 3 = [12/*3]
3f. Naked quint {123**} in R9C7890 + RACA, locked for JR8C7
3g. 16(3) cage at R8C7 = {457} -> R8C8 = 7, R8C79 = {45}, locked for R8 and JR8C7
3h. R8C8 = 7 -> R9CA = *
3i. R7C78 = {38/56), no 4
3j. 4 in JR6C9 only in 15(4) cage at R6CA, locked for CA -> 10(2) cage at R4CA = [82], 8(2) cage at R1CA = [17], R3CA = *, R9CA = *, RACA = 3, R8CA = 6, clean-up: no 2 in R3C7
3k. 3(3) cage at R9C7 = {12*}, 2 locked for R9
3l. 3(3) cage at RAC4 = {12*}, 1,2 and one * locked for RA and JR5C6
3m. Naked triple {678} in RAC789, 7 locked for RA
3n. Naked triple {45*} in RAC123, locked for JR6C1 -> 7(2) cage at R6C1 = {7*}, locked for JR6C1, R9C3 = 3
3o. R7C2 + R8C1 = {12} (hidden pair in JR6C1), CPE no 1,2 in R8C2
3p. R7C78 = {38}, locked for R7, clean-up: no 4 in R6C4
4. R7C6 = 6 (hidden single in JR5C6) -> R6C56 = 8 = {35}, locked for R6 and JR5C6, R8C6 = *, no *s in touching cells, R9C456 = [574]
4a. 6(2) cage at R5C4 = [15], R6C56 = [35], R67CA = [45]
4b. 7(2) cage at R6C4 = {7*}, 7 and one * locked for C4 and JR6C3
5. R2C4 = 8 (hidden single in JR1C1), clean-up: no 1 in R3C7
5a. R1C5 = 8 (hidden single in JR1C5)
5b. R8C3 = 8 (hidden single in JR6C3)
5c. R7C235 = {124} (hidden triple in R7), no *
6. 7 in R1 only in 7(3) cage at R1C2 = [*7*], two *s locked for R1 and JR1C1, no * in R2C5
6a. 7(2) cage at R5C2 = [7*] -> 2(2) cage at R3C3 = [*2], 7(2) cage at R6C1 = [*7], 7(2) cage at R6C4 = [7*], no * in R8C4
6b. R8C24 = [*3] (hidden pair in JR6C3)
6c. 15(5) cage at R3C1 = {12345} (only combination because no *s), no 6
6d. R1C1 = 6 (hidden single in C1)
6e. Naked triple {345} in R1C789, locked for R1 and JR1C7 -> R2C89 = [*6], no * in R3C8, clean-up: no 3 in R3C7
6f. R2C6 = * (other * in R2)
6g. R9C8 = * (other * in C8)
6h. R28C6 = {**}, locked for C6
6i. R13C6 = [23] -> R2C5 = 4, 9(2) cage at R2C7 = [27], 10(2) cage at R3C4 = [46]
6j. Naked pair {12} in R78C5, locked for C5 and JR6C3 -> 3(3) cage at RAC4 = [2*1], R4C45 = [6*]
6k. R3C1 = 2 (hidden single in JR1C1), R8C1 = 1, R7C2 = 2, R78C5 = [12]
6l. Naked triple {345} in R245C1, locked for C1 and JR1C1 -> R234C2 = [351], RAC123 = [*45]
7. R4C7 = * (second * in JR2C7) -> R5C7 = 6 (cage sum), RAC789 = [867], R7C78 = [38]
7a. 3(3) cage at R9C7 = [1*2] -> R6C89 = [21]
7b. R3C8 = 1, R2C8 = * -> R1C78 = 7 = [43]
and the rest is naked singles, without using jigsaw groups or *s.